Biogeochemistry of inland waters

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BIOGEOCHEMISTRY OF INLAND WATERS A DERIVATIVE OF ENCYCLOPEDIA OF INLAND WATERS This page intentionally left blank BIOGEOCHEMISTRY OF INLAND WATERS A DERIVATIVE OF ENCYCLOPEDIA OF INLAND WATERS EDITOR PROFESSOR GENE E. LIKENS Cary Institute of Ecosystem Studies Millbrook, NY, USA Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo Academic Press is an imprint of Elsevier Academic Press is an imprint of Elsevier 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA 30Corporate Drive, Suite 400, Burlington, MA01803, USA 32 Jamestown Road, London, NW1 7BY, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Copyright 2010 Elsevier Inc. All rights reserved Material in this work originally appeared in Encyclopedia of Inland Waters by Gene E. Likens (Elsevier Inc. 2009) The following articles are US Government works in the public domain and are not subject to copyright: VADOSE WATER GROUND WATER GROUNDWATER CHEMISTRY DISSOLVED HUMIC SUBSTANCES: INTERACTIONS WITH ORGANISMS POLLUTION OF AQUATIC ECOSYSTEMS II: HYDROCARBONS, SYNTHETIC ORGANICS, RADIONUCLIDES, HEAVY METALS, ACIDS, AND THERMAL POLLUTION No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elseviers Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: Alternatively you can submit your request online by visiting the Elsevier web site at, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein, Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Biogeochemistry of inland waters : a derivative of Encyclopedia of Inland Waters / editor, Gene E. Likens. p. cm. Includes bibliographical references and index. ISBN 978-0-12-381996-3 (alk. paper) 1. Fresh water. 2. Biogeochemistry. I. Likens, Gene E., 1935- QH541.5.F7.B556 2010 577.614dc22 2010010993 ISBN: 9780123819963 For information on all Academic Press publications visit our website at Printed and bound in China 10 11 12 10 9 8 7 6 5 4 3 2 1 EDITOR Professor Gene E. Likens is an ecologist best known for his discovery, with colleagues, of acid rain in North America, for co-founding the internationally renowned Hubbard Brook Ecosystem Study, and for founding the Institute of Ecosystem Studies, a leading international ecological research and education center. Professor Likens is an educator and advisor at state, national, and international levels. He has been an advisor to two governors in New York State and one in New Hampshire, as well as one U.S. President. He holds faculty positions at Yale, Cornell, Rutgers Universities, State University of New York at Albany, and the University of Connecticut, and has been awarded nine Honorary doctoral Degrees. In addition to being elected a member of the prestigious National Academy of Sciences and the American Philosophical Society, Dr. Likens has been elected to membership in the American Academy of Arts and Sciences, the Royal Swedish Academy of Sciences, Royal Danish Academy of Sciences and Letters, Austrian Academy of Sciences, and an Honorary Member of the British Ecological Society. In June 2002, Professor Likens was awarded the 2001 National Medal of Science, presented at The White House by President G. W. Bush; and in 2003 he was awarded the Blue Planet Prize (with F. H. Bormann) from the Asahi Glass Foundation. Among other awards, in 1993 Professor Likens, with F. H. Bormann, was awarded the Tyler Prize, The World Prize for Environmental Achievement, and in 1994, he was the sole recipient of the Australia Prize for Science and Technology. In 2004, Professor Likens was honored to be in Melbourne, Australia with a Miegunyah Fellowship. He was awarded the first G.E. Hutchinson Medal for excellence in research from The American Society of Limnology and Oceanography in 1982, and the Naumann-Thienemann Medal from the Societas Internationalis Limnologiae, and the Ecological Society of Americas Eminent Ecologist Award in 1995. Professor Likens recently stepped down as President of the International Association of Theoretical and Applied Limnology, and is also a past president of the American Institute of Biological Sciences, the Ecological Society of America, and the American Society of Limnology and Oceanography. He is the author, co-author or editor of 20 books and more than 500 scientific papers. Professor Likens is currently in Australia on a Commonwealth Environment Research Facilities (CERF) Fellowship at the Australian National University. v This page intentionally left blank CONTRIBUTORS J H Aldstadt III University of Wisconsin-Milwaukee, Milwaukee, WI, USA W M Alley U.S. Geological Survey, San Diego, CA, USA J L Ammerman SEAL Analytical, Inc., Mequon Technology Center, Mequon, WI, USA J P Antenucci University of Western Australia, Nedlands, WA, Australia J F Atkinson University of Buffalo, Buffalo, NY, USA D L Bade Kent State University, Kent, OH, USA M T Barbour Tetra Tech, Owings Mills, MD, USA D Bastviken Stockholm University, Stockholm, Sweden L Boegman Queens University, Kingston, ON, Canada B Boehrer UFZ Helmholtz Centre for Environmental Research, Magdeburg, Germany H A Bootsma University of Wisconsin-Milwaukee, Milwaukee, WI, USA P A Bukaveckas Virginia Commonwealth University, Richmond, VA, USA N Caraco Cary Institute of Ecosystem Studies, Millbrook, NY, USA M J Coates Deakin University, Warrnambool, Vic., Australia J J Cole Cary Institute of Ecosystem Studies, Millbrook, NY, USA D J Conley Lund University, Lund, Sweden C S Cronan University of Maine, Orono, ME, USA E A Dreelin Michigan State University, East Lansing, MI, USA K R Echols US Geological Survey, Columbia, MO, USA M C Feller University of British Columbia, Vancouver, BC, Canada K Fienberg University of Minnesota, Minneapolis, MN, USA A M Folkard Lancaster University, Lancaster, UK E Foufoula-Georgiou University of Minnesota, Minneapolis, MN, USA W Geller UFZ Helmholtz Center for Environmental Research, Magdeburg, Germany A E Giblin Marine Biological Laboratory, Woods Hole, MA, USA C Gilmour Smithsonian Environmental Research Center, Edgewater, MD, USA D S Glazier Juniata College, Huntingdon, PA, USA C R Goldman University of California, Davis, CA, USA E M Gross University of Konstanz, Konstanz, Germany vii G Harris Lancaster University, UK J Hauxwell DNR Science Operations Center, Madison, WI, USA B R Hodges University of Texas at Austin, Austin, TX, USA G Hornberger Vanderbilt University, Nashville, TN, USA R Howarth Cornell University, Ithaca, NY, USA J A Hubbart University of Missouri, Columbia, MO, USA J R Jones University of Missouri, Columbia, MO, USA N O G Jrgensen University of Copenhagen, Fredericksberg, Denmark P Y Julien Colorado State University, Fort Collins, CO, USA G Katul Duke University, Durham, NC, USA S S Kaushal University of Maryland Center for Environmental Science, Solomons, MD, USA R Kipfer Swiss Federal Institute of Environmental Science and Technology (Eawag), Swiss Federal Institute of Technology (ETH), Ueberlandstr, Duebendorf, Switzerland S Knight University of Wisconsin Trout Lake Station and Wisconsin Department of Natural Resources, Boulder Junction, WI, USA H-P Kozerski Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany J W LaBaugh U.S. Geological Survey, Reston, VA, USA W M Lewis University of Colorado, Boulder, CO, USA A Lorke University of Koblenz-Landau, Landau/Pfaly, Germany S MacIntyre University of California, Santa Barbara, CA, USA R W Marino Cornell University, Ithaca, NY, USA M D Mattson Massachusetts Department of Environmental Protection, Worcester, MA, USA R M McNinch Michigan State University, East Lansing, MI, USA J C Meadows US Geological Survey, Columbia, MO, USA R Menzel Humboldt Universita t zu Berlin, Berlin, Germany M Meybeck Universite Pierre et Marie Curie, Paris, France E Michael Perdue Georgia Institute of Technology, Atlanta, GA, USA S G Monismith Stanford University, Stanford, CA, USA T N Narasimhan University of California at Berkeley, CA, USA H M Nepf Massachusetts Institute of Technology, Cambridge, MA, USA J R Nimmo U.S. Geological Survey, Menlo Park, CA, USA R H Norris University of Canberra, Canberra, ACT, Australia K Novick Duke University, Durham, NC, USA Y Olsen Norwegian University of Science and Technology, Trondheim, Norway C E Orazio US Geological Survey, Columbia, MO, USA F Peeters Universita t Konstanz, Mainaustrasse, Konstanz, Germany Y T Prairie Universite du Que bec a` Montre al, Montre al, QC, Canada E Prepas Lakehead University, Thunder Bay, ON, Canada G Putz Lakehead University, Thunder Bay, ON, Canada V H Resh University of California, Berkeley, CA, USA C S Reynolds Centre of Ecology and Hydrology and Freshwater Biological Association, Cumbria, UK viii Contributors B L Rhoads University of Illinois at Urbana-Champaign, Urbana, IL, USA G Riedel Smithsonian Environmental Research Center, Edgewater, MD, USA J B Rose Michigan State University, East Lansing, MI, USA F J Rueda Universidad de Granada, Granada, Spain M Schultze UFZ Helmholtz Center for Environmental Research, Magdeburg, Germany N Serediak Lakehead University, Thunder Bay, ON, Canada R W Sheibley Washington Water Science Center, Tacoma, WA, USA D W Smith Lakehead University, Thunder Bay, ON, Canada V H Smith University of Kansas, Lawrence, KS, USA M Sndergaard University of Aarhus, Denmark C E W Steinberg Humboldt Universita t zu Berlin, Berlin, Germany R W Sterner University of Minnesota, St. Paul, MN, USA K M Stewart State University of New York, Buffalo, NY, USA E Struyf Lund University, Lund, Sweden A N Sukhodolov Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany M A Timofeyev Baikalean Research Centre, Irkutsk, Russia R W Tiner University of Massachusetts, Amherst, MA, USA L J Tranvik Uppsala University, Uppsala, Sweden H M Valett Virginia Tech, Blacksburg, VA, USA A V Va ha talo University of Helsinki, Helsinki, Finland J Vidal Universidad de Granada, Granada, Spain W F Vincent Laval University, Quebec City, QC, Canada E von Wachenfeldt Uppsala University, Uppsala, Sweden C J Watras Wisconsin Department of Natural Resources, Madison, WI, USA F M Wilhelm University of Idaho, Moscow, ID, USA T C Winter US Geological Survey, Denver, CO, USA E Wohl Department of Geosciences, Colorado State University, Ft. Collins, CO, USA A Wu est Eawag, Surface Waters Research and Management, Kastanienbaum, Switzerland Contributors ix This page intentionally left blank CONTENTS Editor v Contributors viiix Introduction to the Biogeochemistry of Inland Waters and Factors Affecting Flux and Cycling of Chemicals xvxvi PROPERTIES OF WATER Chemical Properties of Water J H Aldstadt III, H A Bootsma, and J L Ammerman 1 Physical Properties of Water K M Stewart 10 Pressure J F Atkinson 17 Gas Exchange at the AirWater Interface D L Bade 28 Light, Photolytic Reactivity and Chemical Products A V Va ha talo 37 HYDROLOGY Hydrological Cycle and Water Budgets T N Narasimhan 51 Atmospheric Water and Precipitation K Fienberg and E Foufoula-Georgiou 58 Snow and Ice G Hornberger and T C Winter 68 Evapotranspiration G Katul and K Novick 69 Vadose Water J R Nimmo 76 Ground Water W M Alley 88 Ground Water and Surface Water Interaction H M Valett and R W Sheibley 95 Groundwater Chemistry J W LaBaugh 107 Fluvial Export M Meybeck 118 Fluvial Transport of Suspended Solids P Y Julien 131 Streams E Wohl 134 Rivers P A Bukaveckas 143 Springs D S Glazier 155 Wetland Hydrology R W Tiner 177 xi HYDRODYNAMICS AND MIXING IN LAKES, RESERVOIRS, WETLANDS AND RIVERS Biological-Physical Interactions C S Reynolds 189 Density Stratification and Stability B Boehrer and M Schultze 196 The Surface Mixed Layer in Lakes and Reservoirs S G Monismith and S MacIntyre 207 Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes A Wu est and A Lorke 222 The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) A Lorke and S MacIntyre 230 Currents in Rivers A N Sukhodolov, H-P Kozerski, and B L Rhoads 239 Currents in Stratified Water Bodies 1: Density-Driven Flows F Peeters and R Kipfer 247 Currents in Stratified Water Bodies 2: Internal Waves L Boegman 256 Currents in Stratified Water Bodies 3: Effects of Rotation J P Antenucci 277 Currents in the Upper Mixed Layer and in Unstratified Water Bodies F J Rueda and J Vidal 286 Flow in Wetlands and Macrophyte Beds A M Folkard and M J Coates 301 Flow Modification by Submerged Vegetation H M Nepf 313 Hydrodynamical Modeling B R Hodges 320 INORGANIC CHEMICALS: CYCLES AND ECOSYSTEM DYNAMICS Chemical Fluxes and Dynamics in River and Stream Ecosystems W M Lewis 335 Dissolved CO2 J J Cole and Y T Prairie 343 Alkalinity M D Mattson 348 Major Cations (Ca, Mg, Na, K, Al) C S Cronan 354 Chloride S S Kaushal 361 Iron and Manganese A E Giblin 368 Micronutrient Elements (Co, Mo, Mn, Zn, Cu) C R Goldman 378 Biogeochemistry of Trace Metals and Mettaloids C Gilmour and G Riedel 383 Nitrogen Fixation R W Marino and R Howarth 392 Nitrogen R Howarth 400 Phosphorus N Caraco 408 Silica D J Conley and E Struyf 414 Salinity G Harris 418 ORGANIC COMPOUNDS: CYCLES AND DYNAMICS Allelochemical Reactions E M Gross 425 Carbohydrates N O G Jrgensen 437 Carbon, Unifying Currency Y T Prairie and J J Cole 453 Dissolved Humic Substances: Interactions with Organisms C E W Steinberg, M A Timofeyev, and R Menzel 457 xii Contents Interactions of Dissolved Organic Matter and Humic Substances L J Tranvik and E von Wachenfeldt 464 Lipids Y Olsen 471 Methane D Bastviken 480 Natural Organic Matter E Michael Perdue 503 Organic Nitrogen N O G Jrgensen 517 Nutrient Stoichiometry in Aquatic Ecosystems R W Sterner 537 Redox Potential M Sndergaard 549 POLLUTION AND REMEDIATION Acidification W Geller and M Schultze 557 Aquatic Ecosystems and Human Health R M McNinch, J B Rose, and E A Dreelin 569 Bioassessment of Aquatic Ecosystems R H Norris and M T Barbour 577 Deforestation and Nutrient Loading to Fresh Waters M C Feller 585 Distribution and Abundance of Aquatic Plants Human Impacts S Knight and J Hauxwell 601 Effects of Climate Change on Lakes W F Vincent 611 Eutrophication V H Smith 617 Fires E Prepas, N Serediak, G Putz, and D W Smith 630 Floods J A Hubbart and J R Jones 644 Mercury Pollution in Remote Fresh Waters C J Watras 648 Pollution of Aquatic Ecosystems I F M Wilhelm 658 Pollution of Aquatic Ecosystems II: Hydrocarbons, Synthetic Organics, Radionuclides, Heavy Metals, Acids, and Thermal Pollution K R Echols, J C Meadows, and C E Orazio 668 Vector-Borne Diseases of Freshwater Habitats V H Resh 677 Index 687 Contents xiii This page intentionally left blank INTRODUCTION TO THE BIOGEOCHEMISTRY OF INLAND WATERS AND FACTORS AFFECTING FLUX AND CYCLING OF CHEMICALS Biogeochemistry is a multidisciplinary approach to the study of the transformation, flux, and cycling of chemical compounds in aquatic and terrestrial ecosystems (e.g., Likens et al., 1977; Likens and Bormann, 1995; Schlesinger, 1997). The science of biogeochemistry combines aspects of biology, ecology, geology, chemistry, and often hydrology and meteorology. Cycling of elements occurs within the boundaries of an ecosystem, whereas flux refers to the transfer of materials across the boundaries of an ecosystem (Likens, 1992). Conceptual models are informative for thinking about and, in particular, quantifying these complicated transformations, linkages, interactions, and fluxes (Figure 1). Materials moving across the boundaries of an ecosystem represent the biogeochemical connections of that particular ecosystem with the remainder of the biosphere and provide critical points for management interventions (Bormann and Likens, 1967). For example, inputs of acidic materials from the atmosphere (acid deposition) can degrade aquatic and terrestrial ecosystems. Federal legislation in the United States (Clean Air Act Amendments of 1990) was passed to reduce these inputs and their impact on the structure and function of recipient ecosystems. Likewise, outputs from the drainage basin (watershed-ecosystem) of waste water or agricultural or industrial chemicals can pollute or eutrophy receiving systems such as rivers flowing into a lake or estuary. Management interventions using this under- standing can then be taken to reduce these impacts. This volume contains seven sections: first, a brief introduction to the biogeochemistry of inland waters and the factors affecting the flux and cycling of chemicals; second, the properties of water that impact on the biogeochemistry of an ecosystem; third, the hydrologic factors that affect biogeochemical flux and cycling; fourth, the hydrodynamics and mixing in lakes, reservoirs, wetlands, and rivers that are important to biogeo- chemical dynamics; fifth, the cycles and ecosystem dynamics of inorganic chemicals; sixth, the cycles and Figure 1 A conceptual model of the major biogeochemical relationships for a terrestrial ecosystem Bormann FH and Likens GE (1967), Reprinted with permission from AAAS. xv ecosystem dynamics of organic compounds; and seventh, pollution and remediation of the biogeochemical components of aquatic ecosystems. As such, the contents of this book are broadly drawn to cover a wide variety of topics related to biogeochemistry. The articles in this volume are reproduced from the Encyclopedia of Inland Waters (Likens, 2009). I thank the authors of the articles in this volume for their excellent and up-to-date coverage of this important topic. Gene E. Likens Cary Institute of Ecosystem Studies Millbrook, NY December 2009 References Cited/Further Reading: Bormann FH and Likens GE (1967) Nutrient cycling. Science 155(3761): 424429. Hutchinson GE (1950) The biogeochemistry of vertebrate excretion. Bulletin of the American Museum of Natural History 96: 554. Likens GE (1992) The Ecosystem Approach: Its Use and Abuse. Excellence in Ecology, vol. 3, p. 167. Germany: Ecology Institute, Oldendorf/Luhe. Likens GE (ed.) (2009) Encyclopedia of Inland Waters, 3 vols. Oxford, UK: Elsevier/Academic Press. Likens GE and Bormann FH (1995) Biogeochemistry of a Forested Ecosystem, 2nd edn., p. 159. New York: Springer. Likens GE, Bormann FH, Pierce RS, Eaton JS, and Johnson NM (1977) Biogeochemistry of a Forested Ecosystem, p. 146. New York: Springer. Schlesinger WH (1997) Biogeochemistry: An Analysis of Global Change, 2nd edn., p. 588. London: Academic Press. Vernadsky WI (1945) The biosphere and the noosphere. American Scientist 33(1): 112. xvi Introduction to the Biogeochemistry of Inland Waters PROPERTIES OF WATER Contents Chemical Properties of Water Physical Properties of Water Pressure Gas Exchange at the Air-Water Interface Light, Photolytic Reactivity and Chemical Products Chemical Properties of Water J H Aldstadt III and H A Bootsma, University of Wisconsin-Milwaukee, Milwaukee, WI, USA J L Ammerman, SEAL Analytical, Inc., Mequon Technology Center, Mequon, WI, USA 2009 Elsevier Inc. All rights reserved. Water is H2O, hydrogen two parts, oxygen one, but there is also a third thing, that makes it water and nobody knows what it is. D.H. Lawrence (1929) Introduction Water is the most abundant molecule on Earth. In spite of being so common, water is quite unusual from its high melting and boiling points to its tremen- dous solvating power, high surface tension, and the largest dielectric constant of any liquid. In this article, we present an overview of the chemical properties of water. The phrase chemical property is context dependent, which we define in general as a descrip- tion of the way that a substance changes its identity in the formation of other substances. A universally accepted set of chemical properties does not exist in the same way that there is, more or less, a standard set of physical properties for a given substance. Whereas a given substance has intrinsic physical properties (such as melting point), by our definition chemical properties are clearly tied to change. In addition to reactivity, a substances chemical properties also typically include its electronegativity, ionization potential, preferred oxidation state(s), coordination behavior, and the types of bonding (e.g., ionic, cova- lent) in which it participates. Because these properties are extensively studied in general chemistry courses, we will not further discuss them here. Rather, we move beyond the basic general chemistry concepts and focus upon water in a limnologic context par- ticularly, its bulk fluid structure and aspects of its chemical reactivity in the hydrosphere. In the following pages, we begin by briefly review- ing the molecular structure of water and then discuss models for its structure in bulk solution. We then turn our attention to the hydration of ions and an overview of important reactions that involve water, including acidbase, complexation, precipitation, and electron transfer. We conclude with a look at trends in the chemical composition of freshwater that are fundamental to the field of limnology. The Structure of Water Knowledge of the structure of water is the basis for understanding its unique chemical and physical properties. Like the other nonmetallic hydrides of the Group 16 elements, water is a triatomic molecule that forms a nonlinear structure. In terms of group theory, water has two planes of symmetry and a twofold rotation axis and is therefore assigned point-group C2v. The HOH angle is 104.5 , formed as a result of the distortion of the OH bond axes by the two pairs of nonbonding electrons on the oxygen atom. Although water is often described as having four sp3 - hybridized molecular orbitals in a slightly distorted tetrahedral geometry, models based solely upon that configuration fail to accurately predict the properties of liquid water, particularly the extent and influence of hydrogen bonding on the structure of the bulk fluid state. However, a tetrahedral geometry is in fact pres- ent in the solid state, giving rise to the sixfold axis of symmetry that is characteristic of ice, and in large part as the basis of the networks that form in the bulk liquid, though in a rapidly fluctuating dynamic state. Models for the bulk fluid structure of water are a function of the noncovalent van der Waals forces that exist between water molecules. There are five major types of van der Waals forces that occur between neutral molecules and ions in solution: 1 (1) London (or dispersion) forces, in which transient dipoles form by variations in electron density between neutral molecules; (2) Debye forces, in which the dipole of a molecule induces the formation of a dipole in an adjacent neutral molecule; (3) Keesom forces, which form between neighboring dipoles; (4) Coulombic forces, the electrostatic attraction (and repulsion) of ions; and (5) hydrogen bonds, which involve the electrophilic attraction of a proton to electronegative atoms such as oxygen and nitro- gen. All of these forces are present in aqueous solu- tion to varying degrees hydrogen bonding being the most dominant. The high negative charge density of the oxygen atom relative to the high positive charge density of the hydrogen atom creates a large (1.84 D) electric dipole moment for the water molecule (Figure 1). Because of the large dipole moment, the partial positive charge on the H atom is attracted to electron density, while the partial negative charge on the O atom causes the attraction of electrophilic H atoms. In this way, hydrogen bonds are formed, representing the strongest of the van der Waals forces that exist between neutral molecules. While each hydrogen bond is $20 times weaker than a typical covalent bond, each water molecule can participate in multiple hydrogen bonds one to each H atom and one (or more) to each nonbonded pair of electrons on the O atom. The key to understanding the structure of bulk water and its abnormal properties is understand- ing the way that noncovalent hydrogen bonds affect its intermolecular interactions. Although one might expect that the random translational motion of mole- cules in a liquid results in an amorphous structure, the extensive network of hydrogen-bonded molecules in the liquid state of water gives rise to a surprisingly very high degree of order. Water has considerable short-range order that continues to a distance of at least $1015 A from the 2.75 A diameter water molecule. Hydrogen bonds are certainly not peculiar to water, but in water they form such elaborate, extensive, and strong networks that they create a bulk structure with significant order, order that is in fact maintained up to its boiling point. A great deal of research has been devoted to improving our understanding of waters structure in condensed phases broadly divided into studies of short-range and long-range order, the latter defined as beyond $15 A . These research endeavors have been both theoretical and empirical, with theoreticians employing advanced computational tools for mole- cular modeling, and experimentalists armed with a wide variety of spectroscopic techniques. Models for the structure of water in the solid phase (i.e., in the various ices that can form) generate little controversy because theoretical models can be directly verified by crystallographic and neutron-scattering techni- ques. Because of the much more limited atomic motion in the solid state, crystallographic methods have provided an accurate picture of the various ices that form as a function of temperature and pressure. The most common type of ice under ambient condi- tions is hexameric ice, in which six water molecules are hydrogen bonded to form a hexagonal ring, as shown in Figure 2. The most stable state for this structure is a so-called chair conformation (analo- gous to cyclohexane), in which HOH bonds alter- nate around the ring (where is a covalent bond and is a hydrogen bond). Also shown in Figure 2 is the boat conformation, an energetically less stable con- formation than the chair structure. Each O atom has a nearly tetrahedral arrangement of H atoms O O O O OO H H H H H H H H H H H H O O O O O O H H H H H H H H H H H H Figure 2 The arrangement of hexagonal water into a chair conformation (top) and less stable boat conformation (bottom). (a) (b) (c) O HH O HH Figure 1 (a) The distribution of electron density in molecular water (red = high, blue = low). Representation of the electric dipolar nature of molecular water, as contributing dipoles along each OH axis (b) and as a net dipole (c). 2 Properties of Water _ Chemical Properties of Water surrounding it, in which two H atoms are covalently bonded and two noncovalently as hydrogen bonds. The sixfold axis of symmetry found in ice (Figure 3) is the result of the building blocks of cyclic hexamers. Unlike models for ice, much controversy continues to surround models for the structure of liquid water. This may be somewhat surprising given that water is a simple molecule, yet general agreement on a realistic model remains elusive despite the applica- tion of powerful computational and experimental approaches. Predicting the precise arrangements of hydrogen-bonded neighboring water molecules is challenging because the structures are in a state of rapid flux (at subpicosecond timescales). Some insight into the structure of bulk water can be gleaned by examining the structural changes that occur upon the melting of ice. When ice melts, the increase in temperature causes a slight disruption of the hydro- gen-bonded network, thereby initially causing the ice crystalline lattice to collapse. Whereas the structure of ice is >80% ordered, only an $10% decrease in order occurs upon transition to the liquid phase. In this way, much if not most of the short-range order is maintained, which in fact continues to persist in part all of the way to the boiling point at 100 C, where the order is essentially lost completely. The partial collapse of the ordered environment during melting results in slightly more compact hexameric chairs. Consequently, water has the very unusual property of maximal density at a temperature that is higher than its melting point. Above 4 C, further disruption of the intricate networks of cyclic hexamers by more intensive thermal agitation causes the structures to become more open with a consequent decrease in waters density. Water forms clusters in the liquid state. The pres- ence of ice-like structures in water, based on not only hexameric but also pentameric and octameric building blocks, along with free swimming water molecules in more amorphous regions, is the gener- ally accepted model (Figure 4). However, there have been intriguing studies that suggest that there are regions that are far more complex than the structures analogous to ice. Curiously, one of the earliest is found in Platos dialogue Timaeus, where the ancient Greeks classification of matter Earth, Fire, Air, and Water is described in mathematical (geometric) terms. In the Platonic conception of substance, mat- ter is intrinsically composed of triangles. Earth is cubic (i.e., two equilateral triangles each comprising six faces), Fire is tetrahedral (four triangles), and Air is octahedral (eight triangles). In Platos view, water is the most complex structure, taking the form of an icosahedron. A regular icosahedron has 20 faces, with five equilateral triangles meeting at each of the 12 vertices. Thus, along with the dodecahedron, these regular convex polyhedra comprise the famous Platonic Solids. This ancient conception of water may seem quaint, yet it is strikingly similar in concept to several recent theoretical models of the structure of water in the bulk liquid phase. Clusters based on dodecahedra and icosahedra have been proposed by molecular modeling and supported by experiment to exist in water though the evidence remains some- what controversial. Early work by Searcy and Fenn on protonated water clusters by molecular beam mass spectrometry found that a large peak in the spectrum, which corresponded to 21 water molecules (a so-called magic number) was present, that is, for a cluster of unusual stability. Speculation arose that the structure of this magic cluster was a dodecahedral complex of 20 water molecules, each vertex occupied by an oxygen atom and a hydronium ion trapped within (e.g., as in clathrates). Recent work by Dougherty and Howard has indeed found evidence for dodeca- hedral clusters, and Chaplin has proposed a theoreti- cal model for the formation of icosahedral clusters, a model that has been supported by recent neutron scattering experiments. Solvation by Water Ions in aqueous solution interact with one another and with other nonelectrolytes, and their presence in waters dipolar electronic field creates relatively strong noncovalent bonds such that the hydrated ion is the form that undergoes further interactions and chemical reactions, and has consequent implica- tions for the rates of these processes. Only in the gas O O O O O O O O O O O O O O O O O O O O O O O O O O Figure 3 The structure of the most common form of ice (hexagonal ice), an arrangement based upon the HOH chair hexamer. Each oxygen atom is at the approximate center of a tetrahedron formed by four other oxygen atoms. The sixfold axis of symmetry is shown in red for a layer of water chairs (black) overlaying another layer (blue). (Hydrogen atoms are not shown for clarity.) Properties of Water _ Chemical Properties of Water 3 phase do bare (unsolvated) ions exist; in the liquid phase, all ions are hydrated to some degree. To appreciate the solvating power of water, the solubility parameter (d) provides a useful measure, defined as the ratio of the energy required to com- pletely break all intermolecular forces that maintain the liquid state. We represent d quantitatively as EV V s where DEV is the total energy required to vaporize a solute. One can think of d as the cohesive energy density of a substance. Of course d correlates strongly with polarity, with water not surprisingly having the highest value of d when compared to other common solvents (Figure 5). Before studying an example of the structure of a hydrated metal ion, we recognize that each water molecule is already solvated to a very high degree of structural complexity. And because of the autoio- nization reaction of water, which we can represent as a net reaction: H2O H OH ; 1 protons and hydroxide ions are formed that also become hydrated. Realistic structures of the reaction [1] products continue to be the subject of debate, but much evidence suggests that a more realistic way to describe the autoionization of water is 6H2O H2O2H H2O3OH 2 Proposed structures for these ions are shown in Figure 6. For convenience, the simplistic products of O O O O O H H HH H H H H H O O OO H H H H H H H H O OO H H HH H H O H H O H H O H H O HH O H H O H H O H H O H H O H H O H H O H H O H H O H HO H H O H H O HH O H H O H H O H H O H H O H H O H H O H H O H H O H H O H H Figure 4 Proposed models for the structure of bulk water. (Top) The flickering cluster model, with ice-like ordered regions (high-lighted in blue) surrounded by amorphous regions where little short-range order is present. Molecular modeling and some experimental evidence suggests that quite complex structures, such as dodecahedra (bottom left) and icosahedra (bottom right), may also exist. 0 5 10 15 20 25 W ater Am m oniaM ethanolEthanol N itrom ethane D im ethylsulfoxide Brom oform N itrobenzene C arbon disulfide C hloroformBenzeneToluene Solubilityparameter(delta) Figure 5 A comparison of Hildebrands solubility parameter (d) for various liquids (25 C). 4 Properties of Water _ Chemical Properties of Water reaction [1] are commonly used in the literature. However, more complex structures, such as those depicted in Figure 6, are themselves not yet fully accepted as realistic. For ions in aqueous solution, the structures formed by hydration reactions are driven by geometric and electronic factors. The number of water molecules that coordinate as ligands to an ion typically varies from four to nine, and is a function of factors that include ion size, the number of vacant orbitals pres- ent, and the degree of ligandligand repulsion. Given the great interest in pollution by toxic metals, our understanding of cation hydration is more extensive than for anions, yet hydration of the latter should not be surprising given the dipolar nature of water as a ligand. In Figure 7, the concentric shell model for the hydration of an ion is illustrated for aluminum ion, which exists under ambient conditions in the 3 oxidation state. Three regions form the shells an inner layer, known as the primary (1 ) shell, an inter- mediate layer known as the secondary (2 ) shell, and a third region comprised of the bulk fluid. The structure of the 1 shell is highly ordered, as shown in Figure 7 for the tricapped trigonal prismatic arrangement of 11 water molecules closely surround- ing the trivalent cation. In the 2 shell, the influence of the Al(III) ions high charge density would create a more loosely held though structurally defined layer. The bulk fluid extends beyond the 2 shell where the range of the ions force field has no apparent effect on the fluid structure. It is important to note that the concentric shell model is simplistic, focusing H O H H O HH O H H O H O H H O H H O H H H O H H O H H O H H H O H H O H H O H H Figure 6 Proton hopping among three water molecules which together constitute a more accurate representation of a hydrated proton (H5O2 ). The center structure is the most energetically stable of the three shown. A more realistic structure for solvated hydroxide ion (H7O4 ) is also shown (right). Hydrogen bonds are denoted by dashes (---). Al3+ Al3+ O O O O O O O O OO O 1 2 Bulk Figure 7 The concentric shell model (left) for the hydration spheres surrounding a cation, showing the primary, secondary, and bulk solution shells. The primary hydration shell of aluminum ion (right), a tricapped trigonal prismatic geometry in which only the O atom positions for the 11 coordinating water molecules are shown. Properties of Water _ Chemical Properties of Water 5 on the strongest inner layers that are present. That is, the model ignores long-range ordering effects, which, because of their weakness, are inherently difficult to study. For example, molecular modeling (theoretical) studies have suggested that for heavy metal ions in aqueous solution, the surrounding water would be affected by the electronic field of the ion to a distance corresponding to several dozen or more layers of water molecules. Only beyond these layers would the bulk water reflect the undisrupted structural state of a pure solution of water. The Reactivity of Water While we may tend to think of water as relatively inert, it is actually a very reactive molecule, with the oxygen atom behaving as a strong electrophile and the protons involved in autoionization reactions. However, waters reactivity is attenuated by its exten- sive hydrogen bonding. The eightfold ratio between waters single relatively heavy (O) atom and two light (H) atoms, and the charge inequity that exists between them, gives rise to a rapid exchange of pro- tons between adjacent water molecules (proton hop- ping). In a pure solution of water, proton hopping among water molecules is constantly occurring at a high rate even at pH 7 where it is slowest, it occurs on the order of 1000 per second (Figure 5). In studies of hydrogen bonding and the solvation of ions by water, the exchange of protons is even faster than the millisecond timescale observed for a bulk solution of pure water. Nevertheless, water is treated as a stable molecule because the net structure (HOH) is maintained in spite of its intrinsic dynamic state. Fundamentally, chemical reactions occur as means for a species (atom, molecule, or ion) to increase its thermodynamic stability. We can generally classify chemical reactions into two broad categories: (1) those that involve changes in oxidation state, and (2) those that involve changes in coordination environment. While the former redox processes stand alone, the latter type of reaction can be divided into acidbase, complexation, and precipitation reac- tions. We can illustrate these three subcategories of coordination reactions by the example of a series of hydrolytic reactions involving the Al(III) ion: Al3 aq H2O AlOH2 aq H aq pK1 8:2 AlOH2 aq H2O AlOH 2aq H aq pK2 19:0 AlOH 2aq H2O AlOH3s H aq pK3 27:0 AlOH3s H2O AlOH 4aq H aq pK4 31:4 (The subscript aq denotes in aqueous solution, a reminder that all of these species are hydrated, the structures of which are not shown.) While none of the reactions above cause changes in oxidation states, all are acidbase reactions because of the generation of a (hydrated) proton. All can be classified as com- plexation reactions as well because of hydroxide ion acting as a ligand in its coordination to the metal cation, with the formation of complex cations and anions (with the exception of the third reaction). For the third reaction, because of the formation of a solid product, we classify it as a precipitation reac- tion. Chemical reactions in the environment that involve water as a reactant or product i.e., each type of reaction illustrated above as well as redox reactions represent an enormous volume of scholarly work; the interested reader is therefore referred to the Further Reading listed at the end of this article and elsewhere in this Encyclopedia. Trends and Patterns in Limnology The chemistry that is mediated by water in natural aquatic systems varies in space and time. Often this variability is expressed in the form of trends and patterns, and by understanding their causes it is possible to gain insight into the mechanisms that control water chemistry. Ultimately, variation in the chemistry of lakes and rivers can be attributed to three controlling factors: (1) physical processes and properties, including lake morphometry, weather, and climate; (2) geologic setting; and (3) biological fac- tors, including the abundance and composition of biota within the water body and its watershed. Each of these factors may in turn be influenced by human activities. A discussion of how these factors influence water chemistry is best facilitated by examining some observed patterns for three important classes: dissolved gases, major ions, and nutrients. Dissolved Gases The dissolved gases of primary interest in most aquatic ecosystems are oxygen and carbon dioxide. Both of these molecules are nonpolar, therefore, as they partition at the airwater interface their hydra- tion by water is minimal and consequently their solu- bility is very low. The only van der Waals forces that act upon them are very weak Debye forces, in which waters strong dipolar field induces a transient dipole in the nonpolar molecules electronic field. These gases are of primary importance because they both influence and reflect biological processes. As a result, 6 Properties of Water _ Chemical Properties of Water they serve as tracers of electron flow (i.e., energy flow) in an ecosystem. Reactions that convert energy into an organic form will reduce CO2. In the case of photosynthesis, energy is derived from light and water is the electron donor, with the resultant pro- duction of O2. CO2 can also be reduced by chemoau- totrophic bacteria, using other alternate electron donors, such as ammonium (NH4 + ), methane (CH4), and hydrogen sulfide (H2S). In each case, anabolic processes result in a loss of dissolved CO2. Con- versely, the decomposition of organic material results in the production of CO2 and the loss of O2, if that gas is available. In general, the balance between car- bon reduction and oxidation in lakes and rivers is controlled by light-driven photosynthesis. This, and the physical exchange of gases between water and the atmosphere, results in deep waters having higher CO2 concentrations and lower dissolved O2 concentra- tions than surface waters. In lakes that are chemically or thermally stratified, the combination of decompo- sition and reduced vertical mixing can result in anoxia in the hypolimnion. In lakes that are well mixed, anoxia will occur in the sediment. Under these conditions, bacteria will use other electron donors in the metabolism of organic carbon. The electron donor used depends on the relative availabil- ity and the Gibbs free energy of reaction resulting from the use of that donor. As a result, a vertical redox gradient is created, in which the various elec- tron acceptors serially decrease with depth. For lakes of a given size and within a geographic/ climatic region, dissolved gas concentrations can vary according to the loading of nutrients and organic carbon. Lakes with high nutrient loads will exhibit large diurnal fluctuations in surface dissolved O2 and CO2 concentrations, because of high photosynthetic rates during the day and high respiration rates at night. Lakes with high organic carbon loads may be persistently supersaturated with CO2 and undersatu- rated with O2. Temperature is a key property that determines the solubility of gases in water (Figure 8). This has ramifi- cations both for the distribution of dissolved gases within lakes, and for the relationship between climate and dissolved gases, especially O2. Within large tem- perate lakes in which plankton metabolism is generally slow, there is usually sufficient dissolved O2 at all depths to support aerobic organisms. Smaller lakes that stratify may develop an anoxic hypolimnion, with the probability of anoxia increasing with the duration of stratification and lake productivity. In trop- ical lakes and rivers, warm temperatures result in lower dissolved O2 saturation concentrations, and higher decomposition rates, making these systems more prone to anoxia than their temperate counterparts. Major Ions Major ions are those that contribute significantly to the salinity of water. Major cations generally include Ca2 ; Mg2 ; Na ; and K , while major anions may include HCO 3 ; CO2 3 ; Cl ; SO2 4 , and sometimes NO 3 All of these species are of course solvated by water, and the concentric shells that are formed may extend relatively far into the bulk water. The absolute and relative abundance of the hydrated major ions in rivers and lakes are controlled by three factors: basin geol- ogy, rainfall, and evaporationcrystallization pro- cesses. Hence geographic variations in major ion composition can be related to one or more of these factors. For example, the relatively low Ca2 concen- trations in lakes and rivers of Precambrian Shield regions of North America and northern Europe are because of the dominance of igneous granite in their watersheds, while the high sodium and chloride con- centrations of lakes in many dry regions is because of evaporative concentration of these salts. Because the above three factors differentially influence various major ions, the salinity and relative abundance and distribution of ions can be used to infer which of these processes is most significant for a given water body (Figure 9). Some exceptions to the pattern shown in Figure 9 occur, especially in Africa, where a combination of intense weathering, low Ca2 concentrations in rock, and evaporative concentration can result in moderately high salinities that are domi- nated by Na and HCO 3 . Nutrients Most algae require a minimum of 14 essential nutri- ents to grow. The nutrient that limits algal growth in a water body depends on the availability of these nutrients relative to algal demand. In most water Temperature O2solubility(moll1) 250 300 350 400 450 500 1050 15 20 25 30 10 12 14 16 18 20 22 24 26 28 CO2solubility(moll1) Figure 8 The solubility of oxygen () and carbon dioxide () in fresh water at a pressure of one atmosphere and an atmospheric CO2 partial pressure of 380 matm. Properties of Water _ Chemical Properties of Water 7 bodies, phosphorus or nitrogen is the limiting nutri- ent, but trace elements such as iron and molybdenum may also be limiting in some systems. The effects of accelerated nutrient loading to lakes and rivers resulting from human activities, referred to as eutrophication, are well documented in the scientific literature, and are not addressed here. Phos- phorus input to lakes and rivers is controlled primar- ily by rock composition and weathering intensity, but the availability of phosphorus to algae is influenced by the availability of other elements, and by biologi- cally mediated processes. In iron-rich waters, inor- ganic phosphorus is bound as insoluble ferric phosphate or adsorbed onto ferric oxides and oxy- hydroxides, and such systems tend to be unproductive and phosphorus limited. In calcareous regions, including the Laurentian Great Lakes, calcium miner- als may serve as a source of phosphorus through weathering, but this phosphorus is often biologically unavailable because of adsorption to minerals such as calcium carbonate and precipitation with calcium to form apatite. The equilibrium between dissolved and particulate phosphorus is influenced by redox potential, with phosphorus dissolution being acceler- ated under anoxic conditions. Such conditions also promote denitrification, through which biologically available nitrate is ultimately reduced to nitrogen gas, which cannot be assimilated by most algae. Over an annual cycle, water column anoxia is more prevalent in tropical lakes than in temperate lakes, increasing phosphorus availability while promoting nitrogen loss. As a result, nitrogen limitation of algae tends to be more common in the tropics. These patterns can be modified by lake depth. In deep lakes, phosphorus is sequestered more efficiently into sediment, and as a result these lakes tend to have a lower concentration of phosphorus in the water column relative to shallow lakes with similar external phosphorus loads. Conclusion Primarily because of an extensive network of hydrogen bonding, water is structurally complex and has very unusual properties. Ions and molecules are solvated by water, and the resulting structures affect their reactivity and hence their toxicity, transport, and fate. Understanding how nutrients and pollutants are transformed by their interaction with water is essential to understanding the dynamics of the Earths hydrosphere. Furthermore, these chemical transfor- mations affect how these compounds are transported to other environmental compartments (e.g., the litho- sphere and biosphere). Water is said to be the most studied molecule. Yet while theory and experiment have greatly improved our knowledge of waters structure, important ques- tions remain only partially answered. In particular, questions concerning the structure of water in the liquid state, specifically how hydrogen bonding deter- mines long-range ordering effects, continue to intrigue researchers. Given the astonishing properties of such a simple molecule, one might conclude that hydrogen bonding is indeed that third thing to which D.H. Lawrence was alluding. See also: Dissolved CO2; Groundwater Chemistry; Major Cations (Ca, Mg, Na, K, Al); Mercury Pollution in Remote Fresh Waters; Physical Properties of Water. Further Reading Baird C and Cann M (2005) Environmental Chemistry, 3rd edn. New York, NY: W.H. Freeman. Barrett J (2003) Inorganic Chemistry in Aqueous Solution. Cambridge, UK: Royal Society of Chemistry. Chaplin MF (2000) A proposal for the structuring of water. Biophysical Chemistry 83: 211221. Cotton FA, Wilkinson G, Murillo CA, and Bochmann M (1999) Advanced Inorganic Chemistry, 6th edn. New York, NY: Wiley- Interscience. Dougherty RC and Howard LN (1998) Equilibrium structural model of liquid water: evidence from heat capacity, spectra, density, and other properties. Journal of Chemical Physics 109: 73797393. Kusalik PG and Svishchev IM (1994) The spatial structure in liquid water. Science 265: 12191221. 1 10 100 1000 10000 100000 Hi Salinity(mgl1) Evaporationand precipitation Rock weathering Rain CaHCO3 HighRainfallLow Rock weathering Rain NaCl Figure 9 Influence of geology and climate on salinity and major ion composition of inland waters. 8 Properties of Water _ Chemical Properties of Water Manahan SE (2005) Environmental Chemistry, 8th edn. Boca Raton, FL: CRC Press. Marcus Y (1985) Ion Solvation. Chichester, UK: Wiley-Interscience. Martell AE and Motekaitis RJ (1989) Coordination chemistry and speciation of Al(III) in aqueous solution. In: Lewis TE (ed.) Envi- ronmental Chemistry and Toxicology of Aluminum, pp. 319. Chelsea, MI: Lewis Publishers. Searcy JQ and Fenn JB (1974) Clustering of water on hydrated protons in a supersonic free jet expansion. Journal of Chemical Physics 61: 52825288. Stumm W and Morgan JJ (1996) Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters, 3rd edn. New York, NY: Wiley-Interscience. VanLoon GW and Duffy SJ (2000) Environmental Chemistry: A Global Perspective. New York, NY: Oxford University Press. Wallqvist A and Mountain RD (1999) Molecular models of water: Derivation and description. Reviews in Computational Chemis- try 13: 183247. Wetzel RG (2001) Limnology: Lake and River Ecosystems, 3rd edn. San Diego, CA: Academic Press. Zwier TS (2004) The structure of protonated water clusters. Science 304: 11191120. Relevant Websites Water Structure and Science by Professor Martin Chaplin, London South Bank University, London, England, UK. The Chemistry of Water by Professor Jill Granger, Sweet Briar College, Sweet Briar, Virginia, USA. The National Institute of Stan- dards and Technologys Chemistry WebBook, Gaithersburg, Maryland, USA. Properties of Water _ Chemical Properties of Water 9 Physical Properties of Water K M Stewart, State University of New York, Buffalo, NY, USA 2009 Elsevier Inc. All rights reserved. Introduction Water is an indispensable and remarkable substance that makes all forms of life possible. Speculation about possible past or present life on other planets within our solar system, or on any extraterrestrial body somewhere within the universe, is conditioned on the evidence for or against the existence of past or present water or ice. Humans can and did survive and evolve without petroleum products (gas and oil) but cannot survive and evolve without water. Water is the most important natural resource. By far the greatest volume ($76%) of water on Earth is in the oceans. A smaller fraction ($21%) is found within sediments and sedimentary rocks. A still smaller fraction ($1% of the overall volume) is fresh water, and of that 1%, about 73% is in the form of ice (mostly contained within the Greenland and Antarctic ice caps), and only about 23% of that 1% is liquid fresh water. If we consider further that about one-fifth of the worlds liquid fresh water is contained within the five St. Lawrence Great Lakes in North America, and another approximately one-fifth is contained within the deepest freshwater lake on Earth, Lake Baikal, in Russia, we are left with an unevenly distributed resource. It is obvious that if the expanding human populations around the world do not conserve and manage this precious resource very carefully, they put themselves at great peril. Liquid water can be formed through some hydro- gen bonding and electrostatic attraction of two slightly positively charged atoms of the gaseous hydrogen (H) and one slightly negatively charged atom of the gaseous oxygen (O) to form one molecule of water (H2O). Figure 1 provides two views of that polar molecule. Figure 1(a) and 1(b) show the some- what lopsided or asymmetrical arrangement of two smaller hydrogen atoms, separated by an angle of $105 , and a larger oxygen atom. Figure 1(a) is a simple ball and spoke representation whereas Figure 1(b) shows the shared electron orbits, positive () and negative () poles, and the number (eight each) of protons and neutrons in the nucleus of the oxygen atom. The relative elemental simplicity of water is some- what deceptive because of the great influence that some of the unusual properties of water have on the physics, chemistry, and biology of the world gener- ally, and on the distribution of life specifically. The following discussion will describe briefly some of these unusual properties and provide examples of how these properties may help us understand the world of inland waters. Density Density may be simply defined as the amount of weight or mass contained in a specific volume. If the volumes of all substances could be standardized to one size, e.g., one cubic centimeter (cm3 ), then a measure of the weight or mass in that fixed volume gives the density. Table 1 lists a few comparative densities (rounded to two decimals) of two liquids (water and mercury) and some selected solids. Density differences in inland waters may be caused by variations in the concentrations of dissolved salts, by changes in the water temperature, and in pressure. For the vast majority of inland lakes, only vertical differences in salt concentrations and temperatures are of significant influence to mixing processes. Fixed or uniform additions of salts to the water tend to cause linear increases in the density of water. In contrast, fixed or uniform changes in the temperature (both below and above 4 C) of water cause nonlinear changes in the density of water (see Table 2). The density of pure water is maximum at a temperature of 4 C (3.98 C to be precise). It is at this temperature that the interatomic and intermolecular motions and intermolecular distances of water molecules are least. One consequence of this reduction is that more mole- cules of H2O can fit into a fixed space at 4 C than at any other temperature. This compaction allows the most mass per unit volume and thus the greatest den- sity. It is especially noteworthy that the temperature at which water has the maximum density is above its freezing point. Because the differences in densities, within a few degrees above and below 4 C, are very slight, it takes relatively little wind energy to induce substantial ver- tical mixing when water temperatures are within those ranges. An example period, for those lakes that become covered with ice in the winter, would be shortly before an ice cover develops and shortly after the ice cover departs. However, it takes much more energy to cause extensive mixing when the den- sity differences are high, such as is common between the usually warm upper waters and colder lower waters of Temperate Zone lakes during summer. The greater the top-to-bottom differences in temperature, the 10 greater the top-to-bottom differences in density and, consequently, greater are the energies required for wind-induced mixing. There is an old, but still valid, cliche in the northern hemisphere that . . . it is cold up north and warm down south. Water temperatures in more northerly Temper- ate Zone lakes tend to average cooler than those of more southerly tropical lakes. Interestingly, although the upper-water summer temperatures in tropical lakes are somewhat higher than those of Temperate Zone lakes, the lower-water temperatures in tropical lakes are substantially higher than those ordinarily found in the lower waters of Temperate Zone lakes. It might there fore seem that there would be an easy top-to- bottom mix of the water in tropical lakes. Indeed some shallow tropical lakes, with only slight top- to-bottom temperature differences, may have this. However, because of the nonlinear increases in water density with temperature, tropical lakes can be surpris- ingly stable and resistant to much vertical mixing. Table 2 provides a listing of some comparative densi- ties. Let us consider two hypothetical lakes with just a 2 C spread between their lower and upper waters. For example, if a Temperate Zone lake in the spring, not long after the ice departed, had lower and upper waters of 4.0 and 6.0 C, respectively, the density difference would be 1.00000 0.99997 0.00003g cm3 . In contrast, a warmer tropical lake whose lower and upper water temperatures may be 26.0 and 28.0 Cs would have density differences that are much greater (0.99681 0.99626 0.00055 g cm3 ). Thus, the top- to-bottom ratio or density difference of these two lakes with a temperature difference of just 2 C would be 55/ 3 or $18 times as great in the tropical lake as in the Temperate Zone lake. The example above is only hypo- thetical but it shows the nonlinear influence of density changes with temperature, a property of water that influences, to varying degrees, the stratification and mixing of lakes around the world. Heat Capacity/Specific Heat Heat is a form of energy and, as such, we can measure changes in the temperature of a given volume of a substance and determine its heat capacity. Water is the common standard used and its heat capacity (arbitrarily defined as the heat needed to increase the temperature of 1 g of water by 1 C) is compara- tively large. When the mass is also considered then the number of calories needed to raise 1 g of a substance by 1 C is termed its specific heat. For water, the value is 1 cal g1 . That quantity may not seem like much but, compared to other materials, the heat capacity or specific heat of water (1.00 cal g1 ) and ammonia + 8+ 8n + 105 (a) (b) 105 Figure 1 Two schematic representations (a) and (b) of a water molecule. (Modified from various sources.) Table 1 Some comparative densities of water and other substances or elements Substance Densities (g cm3 ) Wood Seasoned balsa 0.110.14 Seasoned maple 0.620.75 Seasoned ebony 1.111.33 Water 1.00 Calcium 1.55 Aluminum 2.70 Iron 7.87 Lead 11.34 Mercury 13.55 Uranium 18.95 Platinum 21.45 Information from multiple sources. Table 2 Comparative densities of average ocean water (salinity $35%), freshwater ice, and pure distilled water at different temperatures Temperatures ( C) Densities (g cm3 ) 20.0 1.02760, ocean water (salinity 35%) 0.0 0.9168, freshwater ice 0.0 0.99987, pure water (from here on) 2.0 0.99997 3.984.00 1.00000 6.0 0.99997 8.0 0.99988 10.0 0.99973 12.0 0.99952 14.0 0.99927 16.0 0.99897 18.0 0.99862 20.0 0.99823 22.0 0.99780 24.0 0.99733 26.0 0.99681 28.0 0.99626 30.0 0.99568 32.0 0.99505 Values from Hutchinson (1957), Pinet (1992), and Weast and Astle (1979). Properties of Water _ Physical Properties of Water 11 (1.23 cal g1 ) are much greater than that of most other substances (Table 3). Consequently, these two liquids are commonly used to exchange heat in refrig- erators and air conditioners. Along with its ever changing and mesmerizing aes- thetic qualities, inland waters are of immense impor- tance in the storage and release of heat. In terms of freshwater lakes, the influence of their heat capacity can be seen most easily around very large lakes located in Temperate Zone latitudes and more inner continental areas. It is in these areas that even larger swings in seasonal air temperature would ordinarily occur in the absence of those lakes. Parts of the immediate surrounding areas of Lake Baikal in Russia (this is actually the worlds deepest freshwater lake as well as one with the greatest volume of water) and the five St. Lawrence Great Lakes of North America are prime examples of the thermal buffer- ing these large lakes provide to their surroundings because of their large heat capacity. For humans, this may mean some beneficial eco- nomic consequences as portions of a lakes heat capacity are slowly released or shed to down-wind regions as the fall and winter seasons progress. The immense thermal capacity of Lake Baikal is such that the lake and its immediate environments are roughly 10 C warmer in December and January, and about 7 C cooler in June and July, than in the cities of Irkutsk (about 50 km to the west of the southern half of Lake Baikal) and Ulan-Ude (about 70 km to the east of the lake). Several coastal and near-coastal regions of the St. Lawrence Great Lakes also provide impressive beneficial evidence of the influence of the Great Lakes heat capacity. There may be reduced costs associated with home and business heating in some coastal regions. An extended or milder autum- nal period permits greater production in near-shore plantations of fruit trees and vineyards. Economic benefits may also accrue in some coastal regions of higher terrain during winter, when enhanced snows permit additional winter skiing, snowmobiling, and other winter sports. However, some influences of a lakes heat capacity have detrimental economic consequences. There are costs involved with snow removal, increased vehicu- lar accidents (because of slippery roads), the corro- sion of cars (attributable to road salts), and the potential long-term ecological changes associated with lake and stream salinization. There are also greater heating costs in spring as cooler water bodies extend their cooling influence inland. In late fall and winter, before an ice-cover develops, heavy snows may result when water vapor, being formed by evap- orative processes off a relatively warm lake, is buoyed into much colder Arctic air (northerly Temperate Zone) crossing the lake. The rising water vapors may freeze, coalesce to ice crystals, and be carried down wind to shore areas where they fall out as snow. Perhaps the most dramatic of all the detrimen- tal consequences is seen following the sometimes paralyzing effect of occasional, but intense, lake- effect snow storms of mesoscale proportions. The lake-effect snow storms tend to have their greatest impact at the downwind end of the St. Lawrence Great Lakes after very cold Arctic air (!13 C colder than the temperature of the lake) has moved across a long axis of the lakes and deposited its snows. These deposits or drops of snow may be in a broader synop- tic pattern, but sometimes they are in very narrow bands of thick snow that may bring auto traffic, schools, and businesses to a stop. In the St. Lawrence Great Lakes region of North America, three of the better known areas where unusually heavy deposits of lake-effect snows may occur are (1) portions of the Upper Peninsula of Michigan on the southeastern shore of Lake Superior, (2) the southeasterly and easterly shores of Lake Ontario, especially the Tug Hill Plateau area of New York State, and (3) the easterly end of Lake Erie, around Buffalo, NY. Indeed, the St. Lawrence Great Lakes have been con- sidered weather factories capable of causing twists of climate found in few other parts of the world. Heat of Fusion/Melting This is just the amount of heat exchanged during a phase shift from either liquid water to solid ice, or from solid ice to liquid water. One gram of water at 0.0 C can be converted to ice at 0.0 C if 80 cal (79.72 cal g1 to be precise) are released in the pro- cess. The same quantity, i.e., 80 cal, is required to melt that 1 g of ice back to 1 g of water. No further caloric additions or subtractions are needed to effect the phase shift. Table 3 The specific heat (cal g1 ) of selected substances compared to that of ice, pure water, and ammonia Aluminum 0.215 Copper 0.092 Gold 0.030 Lead 0.030 Silver 0.056 Zinc 0.092 Ethyl alcohol 0.60 Ice (at 0 C) 0.51 Water 1.000 Ammonia 1.23 Information from multiple sources. 12 Properties of Water _ Physical Properties of Water Because of the heat needed to melt ice, researchers might intuitively expect to see a brief but substantial drop in the mean or weighted lake-water temperature when the ice cover of a lake melts in the spring season. For example, assume there is a hypothetical northerly latitude and a 20-m deep lake in late winter (March). Consider that the lake is covered with 50 cm of ice at 0.0 C. Consider further that the weighted mean temperature of the 1950 cm (essentially 1950 g) water column below the ice is 3.0 C. The heat content of that water column would be 5850 cal (1950 g 3 cal g1 5850 cal). Assuming that there are no further gains or losses of heat to the lake, the amount of heat required to melt the ice would be 3680 cal (80 cal g1 50 cm of ice 0.92 g cm1 , allowing for density of pure ice rounded to two deci- mals 3680 cal). If some of the caloric content of the water column could be used to melt all the ice, the total caloric content would drop to 2170 cal (5850 cal 3680 cal 2170 cal). If those 2170 cal were now equally distributed within a 1-cm2 square and 20-m (2000 cm, essentially 2000 g) deep water column, the mean water temperature would need to drop from 3 to 1.08 C (2170 cal/2000 cal 1.08 C). A drop of about 2 C during the melting of ice would be large! As it turns out, the hypothetical example in the above paragraph is not realistic. Some background follows. Many years ago as a graduate student, I took daily measurements of ice thickness and top-to- bottomwater temperatures for two winters and right through the spring ice break up in a Midwestern U.S. lake. From conversations with others, I was told to expect, and did anticipate, a substantial drop in mean water temperature as the ice melted. . . especially in the last few days of ice cover when the ice thinned rapidly. However, I did not measure any big drops in lake temperature and, in retrospect, should not have anticipated them. The reasons researchers do not see large decreases in lake temperatures with ice loss reflect some interacting physics. For example, there may be somewhat differing weather patterns each spring. The ice generally melts over an extended period of time, from several days to several weeks, not suddenly. Half or more of the total ice thickness may be lost from the top of the ice by melting from warming air temperatures above the ice, not necessar- ily from waters that are just above freezing below the ice. Because of its albedo (percent of incoming solar radiation that is reflected back into space) dark or open water generally reflects only a small fraction of the incoming solar radiation, whereas white snow cover on a frozen lake can reflect a large fraction of incident radiation. Indeed, snow cover extending into the spring period can delay the date the ice disappears. However, with increasing amounts of solar radiation, rising air temperatures, melting snows, and darkening ice, the water below the ice may be gaining some heat from solar inputs at the same time it is losing some heat in melting an overlying ice cover. Moral of the story: Do not expect a big drop in mean water tem- perature as an ice cover melts on a lake. Heat of Vaporization/Condensation As was the case for Heat of Fusion/Melting, the heat of vaporization/condensation also represents the amount of heat exchanged during a phase shift. For vaporization, it is the quantity of heat (540 cal g1 ) needed to convert 1 g of water to 1 g of water vapor. The same amount of heat is exchanged or released in the phase shift during the condensation of 1 g water vapor to 1 g of water. Aquatic scientists may be naturally impressed with the large amount of heat exchanged (80 cal g1 ) in the phase shift from water to ice, or from ice to water, but the amount of heat exchanged (540 cal g1 ) in the phase shift from water to water vapor, or water vapor to water is 6.75 times larger (540/80 6.75). Although the importance of this large amount of heat exchange via vaporization or condensation may be underappreciated by humans, it is huge. On a small but critical scale for life, water evaporating off perspiring warm-blooded animals, including humans, helps maintain body temperatures within narrow survivable limits. On a global scale, the seemingly endless phase shifts between liquid water and water vapor in the atmosphere are key determinants in the redistribution of water and heat within the hydrological cycle around the world. Isotopes An isotope is one of two or more forms of the same chemical element. Different isotopes of an element have the same number of protons in the nucleus, giving them the same atomic number, but a different number of neutrons giving each elemental isotope a different atomic weight. Isotopes of the same element have dif- ferent physical properties (melting points, boiling points) and the nuclei of some isotopes are unstable and radioactive. For water (H2O), the elements hydro- gen (atomic number 1) and oxygen (atomic number 16) each have three isotopes: 1 H, 2 H, and 3 H for hydrogen; 16 O, 17 O, and 18 O for oxygen. In nature, the 1 H and 16 O (usually just given as O) isotopes are by far the most common. In water, the water molecule may be given as 1 H2O or hydrogen oxide, 2 H2O or deuterium oxide, and 3 H2O or tritium oxide, the radioactive one. Properties of Water _ Physical Properties of Water 13 Both of the latter two are sometimes called heavy water because of their increased mass. However, the phrase heavy water gained notoriety primarily because of the association of 2 H2O or deuterium oxide, also called the deuterated form of water, in the develop- ment of nuclear weapons. Many elements have iso- topes, but the isotopes of hydrogen and oxygen are of particular interest because fractionation occurs in vaporliquidsolid phase changes. Heavier molecu- lar species tend to be enriched in the condensation phase and lighter molecular species in the vapor phase. Some isotopes can be used to great advantage as tracers in understanding water movements and exchanges within atmospheric, oceanic, lake, stream, and groundwater systems. Sublimation Water is said to be sublimated, sublimed, or undergo sublimation when it passes directly from a solid (ice) stage to a gas (vapor stage) without becoming a liquid in between. The latent heat of sublimation, i.e., the heat required to make the form of water change from ice to a water vapor, is 679 cal g1 . This quantity is larger than the heat required to melt ice (80 cal g1 ) and vaporize water (540 cal g1 ) com- bined (80 540 620 cal g1 ). Because there may be multiple heat sources and sinks (e.g., the air above the ice and the water below the ice) associated with changing ice thickness on frozen Temperate Zone lakes, it is a challenge to assess the quantitative role that sublimation may play in those changes. Some practical effects of sublimation may be visual- ized by observing a reduction in the volume of some dry ice (solid CO2) or camphor. In another example, after several weeks of continuing subfreezing tem- peratures and deep frost, and assuming that no deicing salts were used, sublimation is most likely responsible for the slow disappearance of an ice sheet over the surface of a frozen sidewalk. Sublimation is also the main process by which wet clothes, which were hung out to dry in subfreezing temperatures, may dry. In the latter case, the water on the clothing quickly freezes to ice, but then slowly vaporizes through sublimation, and the clothes dry. In more recent years, freeze-dried vegetables, fruits, and other products (including instant coffee) provide other examples where the prac- tical application of sublimation is utilized to both market and preserve food. Surface Tension and Cohesiveness Surface tension may be regarded as the resistance offered by liquid water to forces attempting to deform or break through the surface film of water. It is an interesting property and, for water, the surface ten- sion measured in Newtons per meter (N m1 ), is high and shows a slight increase as the temperature falls from 100 (0.0589 N m1 ) to 0 C (0.0765 N m1 ). The molecules of water are strongly attracted to each other through their cohesiveness (attraction of like substances). The properties of surface tension and cohesiveness work together in water in shaping the small rounded water droplets seen on a table top or a car windshield. The same properties help to form the slightly flattened to spherically-shaped raindrops as they fall through the air. The primary force for restoring larger wind-gener- ated surface and internal waves of lakes is gravity, but the primary force for restoring the much smaller cap- illary waves or ripples on a lakes surface seems to be surface tension of the water itself. The surface tension of water is sometimes used to advantage in parlor games in which someone claims that he/she can float a more dense (than water) steel needle on less dense water. When the needle is low- ered slowly and carefully with its long axis paralleling the surface of the water, it may be possible to float the needle because the high surface tension of the water may prevent the needle from sinking. Do not try this by lowering one of the sharp ends of the needle first because a point application of the needle will exceed the surface tension of the water film, and the needle will sink rapidly. When responding to a fire call in fire trucks, water is the most common and practical substance used by firemen. Water is cool, it suppresses heat, it puts out fires and sometimes there is much water to spare. However, the high surface tension of water can reduce its effectiveness in suppressing some fires. Surfactants are compounds that reduce the surface tension of water. In their response to a fire call fire- men often quickly attach hoses to street fire hydrants and spray water from that source on a burning struc- ture. Although the addition of tiny quantities of sur- factants to water may help put out fires, it is not practical (or safe) to add surfactants to an entire distribution system of a city. However, the addition of tiny quantities of surfactants to the volume (roughly 1.89 m3 or 500 gallons in the United States) of water being carried in the fire truck would make that truck water wetter. Some combustibles could be penetrated more easily by this wetter water of reduced surface tension and selected fires could be put out more rapidly. There is a specialized community of organisms, sometimes called neuston, associated with the surface film. For many observers of nature, it is always fascinating to see small insects such as pond skaters 14 Properties of Water _ Physical Properties of Water or water-striders (Gerris sp., within the insect Order Hemiptera), and whirligig beetles (Gyrinus sp. and Dineutes sp., within the insect Order Coleoptera), running around on the surface of ponds, sheltered lakes, and some streams. Because of padded ends to the long middle and hind feet of water striders, and the much shortened but paddle-like feet of the whirli- gig beetles, the high surface tension of the water is such that the insects may dimple, but not break through, the surface film. One of the easiest ways of getting popcorn into your mouth is by touching your tongue to some pop- corn in a container. Here again it is the surface tension of the water on your tongue that lets you hold on to the light popcorn easily. Viscosity This property may be thought of as the internal fric- tion or resistance exerted on one substance (gas, liq- uid, or solid) as that substance tries to flow or move through the same or another liquid. One way of visualizing the influence that liquids or semiliquids of progressively greater viscosities might exert would be to take three glass marbles (same diameter and density) and drop one in each of three similar- sized glasses, one glass containing water, one light oil, and one honey, all at the same temperature. The marble would descend quite rapidly in water, more slowly in the light oil, and very much more slowly in the glass of honey. In this example, honey would obviously exert the most friction or resistance to movement through it and have the greatest viscosity. Viscosity is usually measured in poises (N s m2 ) or centipoises ( 0.01 P). Water at 20 C has a viscosity of 0.01002 P or 1.002 cP. The rate of passive descent through a liquid reflects the density of the liquid itself as well as the surface area and density of the substance moving through it. Viscosity changes with water temperature in that viscosities decrease as water temperatures rise and increase as water temperatures fall. Many fish are powerful enough, slippery from mucous on their skin, and shaped so they can slip through water relatively easily. In contrast tiny zooplankton, with multiple projections on their body, are ordinarily challenged as they attempt to move in any direction and particularly so when moving in cool waters. Colligative Properties These are the four special properties of water that are significantly altered or modified when solutes are added to and dissolve in water. The alterations or modifications of a colligative property (regarded as a binding property) may be predictable in dilute solu- tions when the number of solute particles is known. It is the number of solute particles, not their chemical nature, that determines the extent to which a property is modified. The four colligative properties of water are vapor pressure (when water is in equilibrium with its own vapor), osmotic pressure (the pressure controlling the diffusion of a solvent across a semipermeable mem- brane), boiling point (the temperature at which water undergoes a phase shift to a gas), and freezing point (the temperature at which water undergoes a phase shift to a solid). Even at standardized pressures and temperatures, the extent to which a property is modified depends on the number of solute particles added. Generally, if we add a fixed number of solute particles of a sugar or salt to a liter of pure water, there would be some consequences. The vapor pressure would be lowered but the osmotic pressure would rise. The boiling point (also termed boiling-point ele- vation) would be elevated a bit above the usual boiling point of 100.0 C. In the latter case, a watery mixture with solutes (e.g., a well-mixed soup being heated for a meal) would have to get hotter than the boiling point of pure water before it would boil. The free- zing point would be lower than 0.0 C. A practical application of this (also termed freezing-point depres- sion) is easily seen, in parts of the northerly Temperate Zone in winter, following the application of deicing salts to melt the ice and snow on roads and sidewalks. Although not a colligative property as such, a simple increase in physical pressure also lowers the melting point of ice ($0.007 C/atm) and helps form snowballs (when the snow is not too cold) and form a lubricating layer of water under the blade of an ice skate. See also: The Surface Mixed Layer in Lakes and Reservoirs. Further Reading Eichenlaub VL (1979) Weather and climate of the Great Lakes Region, pp. 127. Notre Dame, IN: University of Notre Dame Press. Hutchinson GE (1957) Geography, Physics, and Chemistry. A Treatise on Limnology, vol. I. Chap. 3. New York, NY: John Wiley. Klaff J (2002) Limnology, Inland Water Ecosystems, pp. 3540. Upper Saddle River, NJ: Prentice-Hall. Kozhov MM (1963) Lake Baikal and Its Life, pp. 1519. The Hague, Netherlands: Dr. W. Junk Publishers. van der Leeden F, Troise FL, and Todd DK (1990) The Water Encyclopedia, 2nd edn., pp. 774777, Chelsea, MI: Lewis Publishers. Properties of Water _ Physical Properties of Water 15 Lemmon EW, McLinden MO, and Friend DG (2003) Thermo- physical properties of fluid systems. In: Linstrom PJ and Mallard WG (eds.) NIST Chemical Webbook, NIST Standard Reference Database Number 69. Gaithersburg, MD: National Institute of Standards and Technology. Morgan JJ and Stumm W (1998) Properties. In: Kroschwitz JI and Howe-Grant M (eds.) Encyclopedia of Chemical Technology, 4th edn., vol. 25, pp. 382405. New York, NY: John Wiley. Mortimer CH (2004) Lake Michigan in motion. Responses of an Inland Sea to Weather, Earth-Spin, and Human Activities, p. 143. Madison, WI: University of Wisconsin Press. Pinet PR (1992) Oceanography, An Introduction to the Planet Oceanus, pp. 120128. St. Paul, MN: West Publishers. Scott JT and Ragotzkie RA (1961) The heat budget of an ice- covered inland lake. Tech. Rep. 6. ONR Contract 1202 (07). Madison, WI: Deptartment Meteorology, University of Wisconsin. Voet D, Voet JG, and Pratt CW (1999) Fundamentals of Biochem- istry, pp. 2327. New York, NY: John Wiley. Wallace RA, Sanders GP, and Ferl RJ (1991) Biology. The Science of Life. ch. 2. New York, NY: Harper Collins. Weast RC and Astle MJ (1979) CRC Handbook of Chemistry and Physics, 60th edn. Boca Raton, FL: CRC Press. 16 Properties of Water _ Physical Properties of Water Pressure J F Atkinson, University of Buffalo, Buffalo, NY, USA 2009 Elsevier Inc. All rights reserved. Introduction Pressure is an example of a surface stress (force per unit area), and is important in many problems of fluid mechanics, as well as in a variety of biological responses in natural water bodies. Pressure has an impact on each of the physical, chemical, and bio- logical components of a fluid system. In this article, we deal mostly with the analysis of the physical impacts of pressure, and provide several examples of biological responses to variations in pressure, including algae, fish, and humans. The study of fluid mechanics is ultimately the study of the response of a fluid to applied forces, subject to certain constraints such as continuity, or mass bal- ance, and constitutive functions such as the relation- ship between shear stress and rate of strain. Fluid forces can generally be divided into body forces and surface forces. Body forces act on all the fluid within a defined control volume, or fluid element, while surface forces act on the surface that encloses that volume. Furthermore, the surface forces can be sepa- rated into those that act either normal to, or in the plane of, the surface of interest (Figure 1). Here we consider both forces and stresses. There are many situations in which analysis on the basis of forces is more useful. For example, calculation of forces acting on a pipe bend or forces acting on a sluice gate or canal lock may be needed in the design of a pipe distribution system or for structures in an open chan- nel flow, respectively. For differential analysis of fluid flow, such as would be used in describing details of the velocity distribution, stresses are generally of more direct interest than forces. Stresses acting in the plane of a surface are called shear stresses, and stresses acting perpendicular to a surface are called normal stresses. Normal stress is generally called pressure, and pressure at a point has the same magni- tude in all directions. Although by mathematical con- vention, the normal stress in Figure 1 is considered positive as shown, pointing outwards from the fluid element, pressure is considered positive as a compres- sive stress, since fluids cannot withstand tension forces (this is a fundamental difference between the mechanical description of fluids and solids). Thus, pressure acting on a fluid element as a result of the surrounding fluid is the negative of the normal stress and points inward on all faces of the element. In general, pressure can be divided into two parts, the hydrostatic and dynamic components. Hydrostatic pressure is generated by the force of gravity acting on fluid that lies above a particular point of interest at which the value of pressure is desired, and dynamic pressure is due to the movement of a fluid. As shown below, hydrostatic pressure also can be assumed in many analyses of fluid flow, especially in environmen- tal applications. For so-called Newtonian fluids, which encompass most fluids of practical interest including water, it is assumed that the shear stress is proportional to the rate of strain, which in turn can be approxi- mated by the velocity gradient in the direction normal to the surface on which the shear stress acts. Thus, in a static fluid, or in a fluid that is moving but in which there are no velocity gradients (i.e., no relative motion), the only forces to consider are the body and normal forces. In the present article, although many of the con- cepts apply to fluids in general, it will be assumed that the main fluid of interest is water, either fresh or saline. The main property of interest that pertains to water and is useful for the analysis of pressure dis- tributions is that of incompressibility, meaning that the density of the fluid is not a function of pressure. In addition, a normal right-handed Cartesian coordinate system will be assumed. Hydrostatic Pressure As the name implies, hydrostatic pressure (here denoted by ph) is the pressure that is exerted under conditions of no fluid motion. To understand how ph varies, first consider a small element of fluid within a larger volume of that same fluid (Figure 2). The top of this element is at a depth h below the water surface. Similar to Figure 1, the element has sides dx, dy, and dz, aligned with each of the respective coordinate directions. The forces acting on the element include its own weight and the forces of the surrounding fluid acting on the surface of the element. Since there is no fluid motion, or more precisely, no relative motion of the fluid element with respect to the surround- ing fluid, the only surface force to consider is that of pressure. If the element is to be in equilibrium, and therefore to remain motionless (as a result of Newtons First Law), the forces acting on it in each direction must be in balance. In Figure 2, the sides of the fluid element are num- bered for convenience, with sides 1 and 2 referring to faces with perpendiculars (to the faces) along the 17 x direction, sides 3 and 4 referring to sides with perpendiculars along the y direction, and sides 5 and 6 with perpendiculars along the z direction. Note that the z direction is oriented parallel to the direction of gravity, but points positive upwards. If ph is consid- ered to be the pressure at the center of the element, then pressures along each of the faces can be expressed in terms of ph using a truncated Taylor Series expansion, and force (product of stress and area on which it acts) balances in each of the three coordinate directions may be written as x ph1dy dz ph2dy dz ) ph @ph @x dx 2 ph @ph @x dx 2 1 y ph3dx dz ph4dx dz ) ph @ph @y dy 2 ph @ph @y dy 2 2 z ph5dx dy ph6dx dy g dx dy dz ) ph @ph @z dz 2 ph @ph @z dz 2 g dz 3 where phi is the hydrostatic pressure acting on face i, g is gravitational acceleration, and r is the fluid density. Note that dx, dy, and dz are assumed to be small enough that any variations in phi over the area of the side may be neglected. Equation [3] differs from eqns [1] and [2] only in that the fluid weight is included in the force balance. Simplifying eqns [1][3] results in @ph @x @ph @y 0; @ph @z g 4 where g rg is the specific weight of the fluid. Keeping the assumption of constant density and letting the fluid be water, the pressure on the top of the fluid element in Figure 2 is given by integrating the last part of eqn [4], resulting in p p0 gh, where p0 is the pressure at the water surface, and h z0z is the water depth, where z0 is the elevation at the water surface and z is the elevation at the top of the element. Also note that the weight (W) of the water column above the fluid element is W ghA, where A dx dy is the area of the element. If p0 0 is assumed, then the pressure acting on the top surface of the fluid element in Figure 2 is simply the weight of water sitting above the element, divided by the area (dx dy). Using similar reasoning, the pressure at the water surface is actually given by the weight of air above the surface, per unit area (note that pressure can be defined in terms of weight, whether or not the density is constant, but if density is not constant the weight must be determined by integra- tion of the density distribution). In fact, Newton long ago deduced that air has mass by determining that water could be pumped up a tube by extracting air at the top only to a maximum height of about 33 ft (10 m), since the weight of a column of water 33 ft high weighs approximately the same as a similar column of air stretching through the entire dx dy Normal stress (pressure) Shear stresses (in plane of surface) dz Figure 1 Stresses acting on one surface of a small fluid element. 5 6 4 3 2 1 y x z h Pressure Water surface Weight Figure 2 Forces acting on a small fluid element under static conditions (no fluid motion); forces include the weight of the fluid enclosed by the rectangular surface and the pressure acting on each of the faces (six totally) of the element. 18 Properties of Water _ Pressure atmosphere. Atmospheric pressure changes slightly with weather and with location (elevation), but is usually assumed to be 14.7 psi, 1 atm, or about 101 kPa. For convenience, the pressure at the water surface is often taken as zero, which facilitates the interpretation of pressure in terms of weight of water above a given point of interest. Pressures written with respect to real air pressure as a reference, or boundary condition, are said to be absolute pressures, while pressures written in terms of zero pressure at the water surface are said to be gauge pressures. In absolute terms, pressure at a depth of 33 ft (10 m) is approximately double what it is at the water surface, and pressure increases by 1 atm for every increase in depth of 33 ft. The lowest possible pressure in abso- lute terms is zero, which is the pressure in deep space, while gauge pressures may take negative values (indi- cating a vacuum). In the remainder of this article all pressures will be assumed to be in gauge terms. The relationship between pressure and depth is further illustrated by considering the case where no external forces are applied (except gravity), and in addition it is assumed that density, and therefore specific weight, is constant, as is usually the case with water. Then, a simple integration of eqn [4] gives the general expression for pressure difference between two points at different vertical locations in the fluid, ph ph2 ph1 z z1 z2 5 where z1 and z2 are the two locations at which ph is evaluated (Figure 3). Equation [4] describes the distribution of pressure in a static fluid. In words, pressure in a static fluid is constant on a horizontal plane, and has a gradient in the vertical direction equal to g. In other words, pressure decreases while moving upward in a static fluid, at a rate given by g. Finding the actual pressure at any point requires integrating the last part of eqn [4] while imposing a boundary condition given by a known pressure at some location, as was done above. The direction of the vertical gradient implies that pressure increases while moving down- ward in the fluid. However, pressure may be forced to increase upwards, if a fluid were to be subjected to a downward acceleration with a magnitude greater than g. For example, consider a fluid in a container (so there is no relative movement of fluid particles with respect to each other, i.e., no velocity gradients) subjected to a downward acceleration of magnitude a, while still assuming gravity is effective, in which case an extra force would have to be included in eqn [3]. The last part of eqn [4] would then become @ph @z g 6 and if a > g, the pressure would increase upwards in the fluid. Similarly, if the acceleration was upward, a and g would be additive, and the mag- nitude of the pressure gradient would be greater than g. For a fluid mass in free-fall, there is no effective weight, since there is no resistance to grav- ity, and eqn [3] would result in a zero vertical gradient and pressure would be constant every- where within the falling mass (equal to zero, in gauge pressure terms). For fluids being accelerated in the x or y directions, the appropriate force, or stress would have to be included in either eqn [1] or [2], and in general the corresponding pressure gradient would no longer be zero. If a force were applied to accelerate a fluid in a container in a horizontal direction, say in the x direc- tion with magnitude ax, then eqn [1] would have to include this force and the resulting gradient would be @ph @x x 7 If the container had a surface open to the atmosphere, the gradient in eqn [7] would be exhibited by a gradient in surface elevation (Figure 4), where pres- sure along a horizontal line would be directly propor- tional to water depth, since there is still no relative motion of fluid in any part of the container, relative to fluid in any other part of the container. An example of this type of problem would be a tanker truck carrying water with a free surface and accelerating (or decel- erating) along a highway. Using the above results, it is possible to calculate the maximum acceleration possible before water would spill over the sides of the tank. The situation is similar for a fluid in solid-body rotation. Considering a fluid rotating around a verti- cal axis, applying a similar force balance in the radial ph1 ph2 ph z1 z2 z Pressure distribution z Figure 3 Pressure variations in a static fluid with constant density. Properties of Water _ Pressure 19 direction as was previously done in vertical and hori- zontal directions (eqns [1][3]) results in @ph @r r!2 8 where r is the radial coordinate and o is the angular velocity. Upon integrating eqn [8], assuming constant density, pressure is found to vary parabolically with radial distance, and then considering a surface open to the atmosphere, the fluid surface will take a para- bolic shape as well, since in this case rotation (about a vertical axis) does not affect forces or pressure distri- bution in the vertical direction. Although of interest in many applications of fluid mechanics, situations in which a fluid is artificially accelerated, either line- arly or in rotation, are rare for environmental appli- cations and these situations will not be considered further here. Density Variations When density is not constant, its variation with depth must be known in order to integrate the last part of eqn [4] to obtain the pressure distribution. For example, if density increases linearly with depth, dr/dz k, where k is a (positive) constant, then the pressure variation would be quadratic with depth and ph2 ph1 g k 2 z2 1 z2 2 0z1 z2 ! 9 where r0 is the density at z 0. As previously noted, when working with water, the incompressibility assumption may be applied, so the density is not affected by pressure (density of water becomes a func- tion of pressure only in the deepest parts of oceans), and for inland waters it may be assumed that density depends on temperature and salinity only. This relation- ship is expressed through an equation of state, T; S 10 where T is temperature and S is salinity. For most inland waters, salinity is small enough (or zero) that only tem- perature variations are important. For fresh water, the temperature of maximum density is 4 C, and the varia- tion of density with temperature may be approximated by a parabolic function such as 0 1 0:00663 T 4 2 11 where r0 999.97kgm3 is the density at 4 C and T is in ( C). Independent of any density stratification, eqn [4] must still hold. For example, it can easily be shown that lines of constant density must be horizontal in a static fluid, since equilibrium would not otherwise be possible. To see this, consider a force balance applied to the fluid element as shown in Figure 5. With lines of constant density oriented as shown, r increases while moving along a horizontal line towards the right. According to the last part of eqn [4], the pres- sure would then also increase while moving along a horizontal line to the right (assuming a horizontal water surface), resulting in a non-zero pressure gradi- ent, violating the first part of eqn [4]. This situation is impossible in a static fluid, although it may be possi- ble in a fluid moving in a body of water large enough that the earths rotation (i.e., Coriolis acceleration) could generate a pressure gradient (tilt in water surface) to counter-balance the pressure gradient associated with the horizontal density gradient. Hydrostatic Forces on Submerged Surfaces In addition to development of the fluid equations of motion, understanding of pressure has practical appli- cations in calculating forces acting on submerged objects. In general, both hydrostatic and dynamic Increasing density and pressure Fluid element Lines of constant density (increasing downward) Figure 5 Fluid element in fluid where lines of constant density are tilted. Direction of acceleration h Direction of pressure gradient Figure 4 Response of water surface in a container of fluid of constant density and with a surface open to the atmosphere and being accelerated to the right; along the bottom, p gh, where h is the depth at any location. 20 Properties of Water _ Pressure pressures must be considered, but initially we look at hydrostatic forces only. To start, consider a submerged rectangular planar surface oriented at an angle with respect to horizon- tal, in a fluid as shown in Figure 6 (note that the surface is shown in an oblique view). To simplify the discussion, it is assumed that the fluid has con- stant density, although the general approach here is easily extended to conditions of varying density. As discussed above, the pressure at any depth h is ph gh, which acts perpendicularly on the surface, indicated on the projection of the surface to the right in Figure 6. The differential force acting on a small area element of the surface dA is dF p dA ghB dh(sin )1 , where B is the width of the surface. Note that dA is oriented horizontally and dh is assumed to be small enough that pressure may be assumed to be approximately constant over the area dA. The total pressure force is then obtained by inte- grating between the limits h1 and h2, F B sin 1 2 h2 2 h2 1 12 This force may be decomposed into horizontal and vertical components, Fx F sin B 2 h2 2 h2 1; Fz Fcos B 2 h2 2 h2 1cos 13 where the negative signs indicate forces in the negative coordinate directions. It is useful to note that the pressure at the area centroid of the surface is phc h1 h2 2 14 where phc is the (hydrostatic) pressure at the area centroid. If this pressure acted on the entire area of the surface, given by B(h2h1)(sin )1 , the total force would be identical to the result of eqn [12]. In fact, it can be shown that this is a general result, that the total pressure force on a submerged planar surface may be calculated as the product of the area and the pressure evaluated at the area centroid. It also can be shown (see Further Reading) that the location of the resultant pressure force acts through the cen- troid of the pressure prism defined by the pressure distribution. Similarly, using moment balances it can be shown that the resultant vertical force acting on a horizontal surface passes through the centroid of that area. For submerged curved surfaces, consider forces acting on the control volume designated by the cross-hatched area shown in Figure 7. Applying a force balance in the horizontal direction gives X Fx 0 ) Fsx B 2 h2 2 h2 1 15 where Fsx is the force of the curved surface acting on the control volume in the x direction (pointing to the right), B is the width of the surface into the page, and the right-hand-side of eqn [15] is pressure force acting on the right side of the control volume, given by eqn [12]. In the vertical direction, the force balance gives X Fz 0 ) Fsz h1Bx Vf 16 where Fsz is the force of the curved surface acting on the control volume in the z direction (assumed to point upwards), x is the length of the curved seg- ment projected in the vertical direction, and Vf is the cross-hatched volume. The first term on the right- hand-side of eqn [16] is the pressure force acting on the top surface of the control volume, and the second term is the weight of fluid in the control volume. Equations [15] and [16] show that the forces acting on a curved surface may be calculated by considering the projected areas of the surface in the horizontal and vertical directions. In other words, the shape of qdh Pressure distribution Depth dA B h1 h2 Submerged surface (oblique view) h Figure 6 Hydrostatic forces acting on a submerged planar surface. Properties of Water _ Pressure 21 the surface does not matter, except in so far as it determines the control volume (cross-hatched area in Figure 7). Buoyancy Buoyancy is directly related to hydrostatic pressure, and may be considered as the net upward vertical force due to pressure acting on a submerged object. This result can be seen by considering an arbitrarily shaped object with volume V submerged in a fluid of constant density r (Figure 8). A surface is drawn below the object to illustrate a space defined by verti- cal sides drawn everywhere tangential to the object (this surface is the area of the object projected verti- cally). A volume of fluid Vf is contained within this surface and above the object. The forces acting on the object are the forces of fluid acting on its upper and lower surfaces, F1 and F2, respectively, and the objects weight W. There are no net forces in the horizontal direction because there are no horizontal variations in pressure. It is easily seen (by applying a force balance to the fluid above the object, for exam- ple) that the force F1 is simply the weight of fluid sitting above the object, occupying volume Vf. The force F2 acting on the lower surface is the same as the weight of fluid that would have occupied the volume (V Vf) this can be seen by thinking of a column of fluid with a surface drawn around the lower half of the object and applying the same sort of force balance as above and noting that pressure is the same upwards as downwards. The force balance for the object in the vertical direction is then Vf W V Vf ) W V 17 This result shows that the weight of the object is balanced by the weight of fluid that has been dis- placed by the object. The displaced weight of fluid is called the buoyancy force. It should be emphasized that the depth at which the object rests is arbitrary (unless the density of the ambient fluid varies), as is its shape. The most important consideration here is the displaced volume. If the average density of the object (total mass divided by V) is equal to the density of the fluid, the object will be in equilibrium at any location in the water column. If the objects density is greater than that of the fluid, it will sink until it hits the bottom. If the density is less than that of the fluid, the object will float at the surface, with the degree of submersion depending on the relative difference in densities and the displaced volume. Sometimes refer- ence is made to the submerged weight of an object, which is simply the actual weight minus the weight of displaced fluid in which the object is placed. Buoy- ancy is what allows ships, which are typically made of materials much denser than water, to float. The ship simply has to be designed so that the weight of dis- placed water is greater than the weight of the ship and all its contents. Fsz Fsx h2 h1 Arbitrary curved surface Resultant vertical and horizontal pressure forces acting on planar surfaces Net forces in x and y directions exerted by curved surface on control volume x Figure 7 Pressure forces acting on a curved surface. V Projected area of object in vertical direction (this represents a surface on a horizontal plane) W F1 F2 Vf Figure 8 Object submerged in a fluid of constant density. 22 Properties of Water _ Pressure Applying a force balance to fluid elements in a fluid with density stratification gives rise to the concept of relative buoyancy, where the density of the fluid element is not the same as the density of its surround- ings. There is a net reduced effect of gravity since the weight of the fluid element is partially offset by buoy- ancy. For analysis of these situations, the net effective gravity is referred to as reduced gravity, or relative buoyancy, defined by g0 g 0 18 where Dr is the difference between the density of the element and its surroundings, and r0 is a reference density value (usually taken as that of the surrounding fluid). Reduced gravity appears in problems associated with density-stratified flows, and may take positive or negative values, depending on the sign of Dr. Dynamic Pressure As previously noted, dynamic pressure is associa- ted with fluid motion. The simplest illustration of dynamic pressure is obtained by considering the Bernoulli equation, which for cases of steady flow, constant density, and negligible frictional losses may be written as 2 2g p z H 19 where v is the fluid velocity and H is a constant known as the Bernoulli constant, or total head, and is given by conditions of the problem (i.e., eqn [19] states that total head is constant for a given set of flow conditions). Each of the additive terms in eqn [19] has units of length. The first term is known as the velocity head, the second is the pressure head, and the third is the elevation head, or simply elevation. Definitions of these terms, as well as concepts of hydraulic grade line (HGL) and energy line (EL) for the case of open chan- nel flow are shown in Figure 9. It may be noted that the Bernoulli equation represents a statement of conserva- tion of energy, where H represents the total energy of the flow in units of length, or head. In terms of real energy units, eqn [19] would be multiplied by mass and by g. The EL is a graphical representation of the magnitude of H; so in a system where energy is con- served, the EL, or magnitude of H, is at a constant level when moving from one location to another in the flow. In other words, considering two sections in the flow as in Figure 9, the total head should be the same at both sections, H1 H2 (note that velocity is assumed to be uniform at each cross section in this example more detailed discussion is needed when velocity gradients are considered). The Bernoulli equation is developed for comparison of conditions at difference points along a common streamline, or in the case of irrotational flow as is usually assumed for open channel flow, for any two points in the flow field. By considering a case where velocities are zero everywhere, eqn [19] reduces to a statement of hydrostatic pressure, where (pg1 z) is a constant. This sum is known as piezo- metric head, and constancy of piezometric head (i.e., constant position of the HGL) in a static fluid is easily seen to be consistent with eqn [7]. In a moving fluid there is a sort of inverse relation- ship between velocity and pressure, as indicated in eqn [19]. That is, regions of higher velocity generally have lower pressures, and vice-versa. This is the main effect, for example, that produces lift in airfoils and allows aircraft to fly airfoils are designed so that HGL EL Section 2Section 1 Flow z p1/g v1 2/2g H z2 p2/g v2 2/2g z = 0 (datum) Figure 9 Definition of head terms for Bernoulli equation (eqn [19]). For hydrostatic pressure variations the sum of the elevation and pressure heads is equal to the elevation at the water surface, the position of which is also known as the hydraulic grade line (HGL). The energy line (EL) represents the elevation of total head; in an energy-conserving system the EL is horizontal, but in cases where there is energy loss, as may be induced by friction, the EL slopes downward in the direction of flow (shown as a dashed line). Properties of Water _ Pressure 23 there is a faster flow of air over the top of the airfoil than over the bottom, resulting in lower pressure on the top than on the bottom, with a net upward force resulting. For applications in water flow, a typical problem might involve calculating the pressure force acting on an object submerged in a flow. A simple situation of this type is illustrated in Figure 10, where a flat plate is placed perpendicular to a moving stream of water. At point 1 the velocity is v1, the pressure is p1, and the elevation is z1. At point 2, which is at the surface of the plate, the velocity is (ideally) zero, while the elevation z2 z1. Applying the Bernoulli equation [19] then gives p2 p1 1 2 2 1 20 Point 2 is known as a stagnation point, which is defined anywhere where the velocity is zero, and the second term on the right-hand-side of eqn [20] is the dynamic pressure component. In this case, the dynamic pressure acting at point 2 attains the highest value possible, since point 2 is a stagnation point and v2 0 (any velocity v2 > 0 would reduce p2 by an amount p2 2 =2). When comparing pressures at two points in a fluid, any difference due to different velo- cities comes from a dynamic pressure effect, which depends on the difference in velocities squared (v2 ). In general, to calculate the total pressure force acting on a submerged object would require an integration of the pressure distribution on the surface of the object, which as described previously would require detailed knowledge of the velocity distribution. Fortunately, in many cases a simpler approach may be applied, based on general force balance and continuity consid- erations. For example, consider calculations of force acting on a sluice gate as shown in Figure 11. Again assuming constant velocities at each cross section (1 and 2), an integral momentum equation may be applied, along with the continuity and Bernoulli equa- tions, to solve for the net hydraulic (pressure) force acting on the gate. Considering a control volume con- sisting of the water between sections 1 and 2, and assuming steady flow, continuity states that flow rate of water entering the control section must be the same as that leaving, so 1h1 2h2 21 where unit width has been assumed (i.e., two- dimensional flow is considered for this problem). Using the channel bed as datum and neglecting head loss, the Bernoulli equation gives 2 1 2g h1 2 2 2g h2 22 where h is the piezometric head. If the depths h1 and h2 are known, eqns [21] and [22] can be used to find the velocities at each section, and therefore the flow in the channel. Applying the Reynolds Transport Theorem to evaluate forces on the control volume gives the integral momentum equation pc1h1 pc2h2 Fg q2 1 23 where pc is the (hydrostatic) pressure evaluated at the centroid of each cross section (recall previous discus- sion of forces on submerged surfaces), Fg is the total force exerted by the gate on the fluid in the control volume, assumed to act in the negative x direction, and q vh is the two-dimensional flow rate, or flow per unit width. The force Fg is the net integrated effect of the pressure distribution on the gate, resulting from both hydrostatic and dynamic components, and is found using eqn [23] without needing to actually cal- culate the pressures directly. Thus, with a simple measurement of depths upstream and downstream of the gate, the net force on the gate is found, where the force on the gate is in the opposite direction as the force found from eqn [23]. Pressure in the Equations of Motion In several of the above examples it has been implicitly assumed that the pressure variation was approxi- mately hydrostatic, even in the case where velocity was not zero. This assumption is evaluated in this z1 =z2 (v2 =0) 2v1 1 Figure 10 Dynamic pressure force acting on planar surface in moving stream of water; point 2 is a stagnation point. h2 h1 2 1 v1 v2 Figure 11 Forces acting on a sluice gate in (two-dimensional) open channel flow. 24 Properties of Water _ Pressure section, which explores the impact of pressure differ- ences on the equations of motion, as would be used in developing mathematical models of flows and circu- lation for environmental analyses in lakes and streams. The equations governing fluid flow consist of statements of conservation of mass (continuity), momentum, and energy. Of particular interest here are the momentum equations, or NavierStokes equations, which in component form are written as @u @t u @u @x v @u @y w @u @z fv 1 @p @x r2 u 24 @v @t u @v @x v @v @y w @v @z fu 1 @p @y r2 v 25 @w @t u @w @x v @w @y w @w @z 1 @p @x g r2 w 26 where f is the Coriolis parameter, defined as twice the daily rotation rate of the earth times the sine of the latitude, and n is kinematic viscosity. For inland waters, except for very large lakes such as the Laurentian Great Lakes of North America, the Coriolis term may be neglected. Also, it is easily seen that in the case of no motion, u v w 0, eqns [24][26] reduce to eqn [4]. The main hydrostatic pressure equation refers to the vertical distribution of pressure. In most cases of natural flows, the motions are predominantly in hori- zontal directions, so w is small, as are vertical accelera- tions, so that all terms in eqn [26] are negligible except for the first two terms on the right-hand-side, consis- tent with hydrostatic pressure variation in the vertical direction. There are certain situations where this is not the case, such as during fall or spring overturns in lakes, but these situations are generally of limited temporal duration. It should be noted that assuming a hydro- static pressure variation in the vertical direction does not necessarily imply any assumption for horizontal pressure gradients. For applications in model development for inland waters, it is useful to explore the impact of the pres- sure term in the NavierStokes equations. Here, con- sider the vector form of eqns [24][26] @~v @t ~v :r~v 2~ ~v ~g 1 rp vr2 ~v 27 where ~ is the earths rotation vector. The pressure term, as discussed previously, may be considered as the sum of hydrostatic and dynamic components, where the hydrostatic part may be written as ph pr Zz zr gdz 28 where pr is a reference value at z zr. Note that eqn [28] is simply the integrated form of the last part of eqn [4]. Letting p ph pd, where pd is the dynamic pressure, and substituting eqn [28], the pres- sure gradient term in eqn [27] may be written as 1 rp 1 rpr g r Zz zr dz 1 rpd 1 rpr g Zz zr rdz grz g r rzr 1 rpd 29 Then, substituting eqn [29] into eqn [27] and apply- ing the Boussinesq approximation (neglect density variations except in the buoyancy term), the result is @~v @t ~v:r~v 2~ ~v 1 0 rpr pd g 0 Zz zr rdz grzr vr2 ~v 30 where r0 is a reference density value, usually the density at 4 C in freshwater systems. On the right- hand-side of eqn [30], the gradient of reference pres- sure, pr, may usually be neglected. The second term is the effect of density variations, which are important for stratified fluids, and the third term is the effect of reference surface gradients (such as waves). Along with continuity and energy equations, eqn [30] may serve as a general starting point for developing models of fluid motion in natural waters, although in many instances it is possible to neglect some of the terms and use a simplified form of the equation. Biological Responses The above discussion focuses on the physical descrip- tion of pressure, how it varies in a fluid, how forces are manifested on submerged objects, and how it is incorporated in the equations that would form the basis of hydrodynamic and water quality models of inland waters. Other considerations apply to various species that live or play in water, and examples of issues related to algae, fish, and humans are presented briefly here. For submerged objects buoyancy is the main force of interest. As shown previously, buoyancy is the net result of pressure forces in the vertical direction. Pressures in horizontal directions, or at least in the direction of movement, are of interest in determining drag that must be overcome to maintain such move- ment. The simplest biological response and move- ment in the water column is achieved through the process of buoyancy regulation, which is used by certain species of algae to position themselves opti- mally in regions of preferable temperature, light, and Properties of Water _ Pressure 25 nutrient availability. These algae are mostly of the blue-green type (or cyanobacteria), which also can cause nuisance and even harmful (toxic) blooms. Buoyancy regulation is achieved by increasing or decreasing gas volume in vesicles in the cells. By increasing or decreasing volume, the displaced water and hence the buoyancy force acting on the cell is altered. Increasing volume increases the buoyancy force and causes the cell to rise, and up to five-fold variations in rising or falling rates have been observed. The actual rate of rise depends on the density struc- ture of the water column in which the organism floats, since buoyancy is the weight of the displaced water, which changes as a function of density. For fish the physical interactions with the water environment are more complicated, due to locomo- tion. Some fish make use of a gas-filled cavity, called a swim bladder, or gas bladder, to maintain buoyancy and stability. Additional uplift forces can be obtained by swimming, through the same Bernoulli effect noted above, that allows airplanes to fly. However, this dynamic lift is achieved only when there is for- ward motion. With respect to the swim bladder, in order to maintain a constant buoyancy, the volume of the bladder must remain approximately constant as the fish swims in different depths where pressure changes, and this requires some interesting physiologi- cal responses. Near the surface, the pressure in the water is close to atmospheric pressure, but as previously described, pressure increases by about 1 atm for every 10 m of depth. Unlike water, air is compressible and volume decreases as pressure in- creases, so there is a tendency for reduced buoyancy at greater depths. In order to maintain neutral buoy- ancy within a water column, an effort must be made by the fish with swim bladders to keep the volume of their swim bladder constant. Methods of maintain- ing some hydrostatic equilibrium varies among dif- ferent groups and species of fish. This maintenance is usually done by slight secretions or resorptions of gas within the swim bladder itself, or by release of gas through a duct. Physoclists are fish (e.g., the perch, Perca fluviatilus) that have special gas secret- ing and resorbing sites on the swim bladder wall that let the fish descend or ascend, respectively. Physo- stomes are fish (e.g., the eel, Anguilla anguilla) that have a pneumatic duct that extends from the swim bladder to the esophagus. Such a duct allows these fish to release, or burp some expanding gas as the fish ascends. Still other fish (e.g., castor oil fish, Ruvettus pretiosus) are able to maintain neutral buoyancy through alterations in their quantities of lipid storage. Interestingly, fish like tuna (e.g., the little Pacific mackerel tuna, Euthynmus affinus) and sharks have no swim bladders. This latter group, as well as species like dolphins, gain hydrodynamic lift by their shape, but they must swim continuously to keep from sinking. Perhaps of more direct interest for humans is the attention one must pay to pressure when diving. As a diver moves into deeper or shallower water, the pres- sure changes and affects the balance between concen- trations of gases in the dissolved (liquid) and gaseous phases, following Henrys Law. This law expresses the equilibrium between the dissolved phase concen- tration of a gas and its pressure in the surroundings. In essence, as outside pressure increases, gases are pushed into the dissolved phase. The problem for divers occurs when they ascend too quickly following a deep dive. As pressure is reduced, gases move into the gaseous phase, and if pressure is reduced too rapidly, the gas cannot leave the blood stream quickly enough and gas bubbles, mostly nitrogen, form in the blood. In other words, the re-dissolution process does not have enough time to accommodate the gasses moving out of solution due to the pressure change. This situation leads to the bends, also known as decompression or caisson sickness (the latter defini- tion comes from the situation where workers would work in pressurized caissons, or boxes lowered in streams for construction of structures such as bridge towers the interior of the caisson was pressurized to equal that of the surrounding water to prevent water from entering the work area, and workers leaving the pressurized area too quickly would suffer the same symptoms as divers who ascended too quickly from a dive; this was a significant problem in the building of the Brooklyn Bridge, for example). Symp- toms of the bends include pain in the joints, muscle cramps, sensory system failure, and, in extreme cases, even death. While the material in this article goes into some depth with regard to the scientific and engineering analysis of pressure, it is important to recognize that different species have different responses to pressure variations. The above examples represent only a small sampling of these reactions, and how pressure and its net vertical force, buoyancy, is important in regulating our physical environment. Further Reading Batchelor GK (1967) An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press. Morris HM and Wiggert JM (1972) Applied Hydraulics in Engineering. 2nd edn. New York: Wiley. 26 Properties of Water _ Pressure Munson BR, Young DF, and Okiishi TH (1998) Fundamentals of Fluid Mechamics. 3rd edn. New York: Wiley. Pelster B (1998) Buoyancy. In: Evans DH and Boca R (eds.) The Physiology of Fishes, 2nd edn. Boca Raton, FL: CRC Press. Rubin H and Atkinson J (2001) Environmental Fluid Mechanics. New York: Marcel Dekker, Inc. Shames IH (2003) Mechanics of Fluids. 4th edn. New York: McGraw-Hill. Turner JS (1973) Buoyancy Effects in Fluids. Cambridge: Cambridge University Press. Relevant Websites Diving information and diving tables. Diving information and diving tables. General dis- cussion of water pressure. Calculator for pressure in salt water. Properties of Water _ Pressure 27 Gas Exchange at the AirWater Interface D L Bade, Kent State University, Kent, OH, USA 2009 Elsevier Inc. All rights reserved. Introduction Gas exchange at the airwater interface is a key com- ponent of the biogeochemistry of all aquatic eco- systems. Organisms (e.g., algae and bacteria) can directly influence the flux of gases by controlling their concentrations. Aquatic systems can be a source of gases when they accumulate from biochemical reactions. Or, inland water bodies can act as a sink for gases when they are consumed in biochemical reactions. Release of volatile pollutants will also be controlled by the exchange across the airwater inter- face. The importance of airwater gas exchange is made even more evident in our attempts to understand global carbon cycles and the movement of CO2 between air and sea. Exchange of CO2 and certain other gases, such as CH4, from inland aquatic systems has been shown to be of global significance. Most of the examples in this chapter will be drawn from the knowledge base developed in lakes and oceans. Specif- ically examined will be the gas exchange that is limited by molecular diffusion directly at the airwater inter- face in relatively still bodies of water. Basic Gas Exchange Principles Gas exchange at the airwater interface is influenced by both chemical and physical parameters. The chemical aspects of gas exchange are dominated by the chemi- cal gradient across the airwater interface. These gradi- entscanbeinducedbychangesintemperatureorsalinity, which influence the solubility of the gas, or by chemical or biological processes that produce or consume the gas. Physical factors include the turbulent and molecular diffusion of the gas. Turbulent transport moves gases near the aqueous boundary, where they approach the diffusive sub-layer. In this boundary layer near the sur- face, turbulent forces are attenuated owing to viscous properties of the boundaryanddiffusive transport domi- nates (e.g., Figure 1(a)). Therefore an understanding of these physical and chemical properties is crucial for understanding gas exchange phenomena. Ficks law of diffusion can be used to describe the dependency of gas exchange on chemical and physical properties. From Ficks law, gas flux F [mol m2 day1 ] is given as: F D @C @Z 1 where D is the molecular diffusion coefficient (m2 d1 ) and @C/@Z is the concentration gradient (mol m4 ) across the boundary layer of depth Z (m). Although D can be quantified experimentally, the concentration gra- dient is difficult to measure because Z is extremely small (on the scale of mms). Therefore Ficks law is restated so as to account for the bulk properties of airwater gas exchange. Here the gas flux is defined as: F kDC 2 where k has several names such as, gas transfer velocity or piston velocity or gas exchange coefficient, and units of m day1 or more commonly cm hour1 . The concentrationgradient,DC,isthedifferencebetweenthe concentrations on either side of the boundary. The term piston velocity refers to the rate of approach towards equilibrium of the concentration gradient, and can be conceptualized as the depth of water that is equilibrated with the equilibrium air concentration over the specified period of time. We will now explore the physical and chemical details of gas exchange represented by eqn. [2]. Physical Factors Kinetic energy is transferred to water bodies by several means; most notable for gas exchange in lakes are wind shear and buoyancy flux. In fact, most work on lakes has focused solely on the influence of wind and largely has ignored the possibility of other sources of kinetic energy. This kinetic energy is dissipated as it cascades from large to small turbulent eddies. These eddies cause mixing within the water column, and are responsible for diffusion of mass throughout the mixed-layer of the water column. However, close to the interface between air and water, turbulent eddies and mixing are sup- pressed owing to viscous forces of the water. In the layer near the interface where viscous forces dominate, turbulent diffusivity is decreased and molecular diffusivity dominates. The same situation of a turbulent layer and diffusive sub-layer can be described for the air above the water. Figure 1(a) diagrams the turbulent layers and diffusive sub-layers at a hypothetical airwater interface. An important term, the Schmidt number (Sc), describes the dependence of the diffusive sublayer on kinematic viscosity of the water and molecular diffusivity. The Schmidt number is defined as: Sc n D 3 where n is the kinematic viscosity (m2 day1 ). Kinematic viscosity is the dynamic viscosity divided by the density. 28 Because the diffusivities of gases are generally much decreased in water compared with their diffu- sivities in air, their flux across the airwater interface is most often controlled by the aqueous diffusive sub- layer (Figure 1b). Exceptions occur for those gases that are extremely soluble in water, or react chemi- cally with water (Figure 2c). All of the major con- stituents of the atmosphere are limited in their exchange by the water phase. Mechanistic Models of Gas Transfer Several alternative models have been proposed to explain the mixing and diffusion across the boundary layer of the airwater interface. The earliest of these is the stagnant film model that results directly from eqns. [1] and [2] and is captured in Figure 1. Here, dw (from Figure 1), or analogously, Z (from eqn. [1]), is spatially and temporally constant, and k D Z 4 Considering this model, more turbulent environ- ments have decreased values of Z (the diffusive layer becomes smaller) and an increased gas transfer results. Theoretical and experimental evidence, how- ever, suggests that this relationship is incorrect. How- ever, it provides a useful starting point for evaluating some characteristics of gas exchange. Using this simple model it is possible to see how gas transfer coefficients are related to the Schmidt num- ber, and how gas transfer coefficients can be con- verted from one gas to another. Combining eqns. [3] and [4] for two different gas results in Z n 1 Sc1k1 1 Sc2k2 5 More generally k1 k2 Sc1 Sc2 n 6 where the coefficient n 1 for the stagnant film model, but n may have other values (usually 1/2 or 2/3) depending on the particular model of the bound- ary layer. One model developed, after recognition of short- comings in the stagnant film model, was termed the boundary layer model. Because a distinct discon- tinuity between turbulent and diffusive layers does not actually exist, the boundary layer model describes a smooth transition from turbulent to molecular transport. This model contains the assumption of a rigid smooth surface of the water. The boundary layer model describes the gas exchange coefficient as: k 0:082 ra rw 0:5 Sc0:67 u 7 where ra and rw are the densities of air and water, respectively, and u* is the friction velocity which can be related to wind stress. Note that the Schmidt num- ber exponent for this model is n 2/3. This exponent has been corroborated by empirical evidence under conditions of low wind speed, i.e., the water surface is mostly smooth. Thus, the inherit assumptions of this model make it applicable only under conditions of low wind speed. Another refinement of the stagnant film model is the surface renewal model. This model describes the boundary layer as being influenced by turbulent eddies that bring water from below and periodically renew the water within the surface boundary layer. Cw Ca Ca Ca Ca Water w a Concentration Turbulent layer Turbulent layer Diffusive layer Diffusive layerAir (a) (b) (c) (d) Cw Cw Cw Figure 1 Conceptual diagram of the turbulent layers and diffusive sub-layers at the airwater interface. The depth of the diffusive sublayer in (a) depends on the diffusivity, solubility, and reactivity of the gas in question. The schematic in (b) represents the case for slightly soluble gases that are limited by the aqueous phase boundary. In (c) the gas represented is for a soluble gas and exchange is limited by the air phase. Under conditions chemically enhanced diffusion, the gas can react with water, causing an increased gradient in concentration. Properties of Water _ Gas Exchange at the AirWater Interface 29 The time period (t) required to renew the surface boundary layer is used to determine the gas exchange coefficient by: k D t 0:5 8 In this model the Schmidt number exponent is n 1/2. Empirical evidence suggests that a Schmidt number of 1/2 is appropriate for conditions where the water surface is not smooth. Many elaborations of the surface renewal model exist, and the model is currently quite popular in the field of gas exchange. The flexibility of this model lies in the fact that many turbulent measurements can be used in quantifying the renewal time. This is an important advancement, since other factors besides just wind stress can lead to turbulence in a water column (e.g., convection cur- rents or turbulence generated at sediment or thermo- cline interfaces). In general, the relationship between the gas trans- fer velocity, the Schmidt number and the turbulent parameters can be established as: k Scn f u; l 10 where the Schmidt number describes the thermody- namic conditions, n depends on the characteristics of the waters surface, and f(u,l) describes k as being a function of the hydrodynamics. Specifically, u is the turbulent velocity scale, and l is the turbulent length scale. The turbulent velocity scale is also known as the root mean squared velocity and is the standard deviation of the velocity fluctuations. The turbulent length scale is based on the distance over which velocity fluctuations are correlated with each other. Several important length scales can be determined for water bodies. For instance, large or small eddies can be considered most important for gas exchange, and parameterization for each situ- ation can be made using the general model mentioned earlier. Chemical Factors The concentration gradient across the airwater inter- face, DC, is described in several analogous ways. One way of representing the gradient, as depicted in Figure 1, is in terms of concentrations, DC Cw aCa 11 where a is the dimensionless Ostwald solubility coef- ficient defined as the volume of gas (at a given tem- perature and pressure) dissolved per unit volume of solvent. Subscripts w and a refer to water and air concentrations, respectively. The gradient can also be expressed as DC Cw Kspa 12 where pa is the partial pressure/fugacity of gas in the air in units of atm, and Ks is the solubility coefficient (mol l1 atm1 ). Finally, the gradient is often measured U10 (m s1 ) k(cmhr1 ) 0 2 4 6 8 10 12 14 16 18 1086420 Figure 2 Models of k600 related to wind speed at 10 m (U10): solid line, Wanninkhof (1992); dashed line, Cole and Caraco (1998); dotted-dashed line, Crusius and Wanninkhof (2003) (their first model presented in Table 3); and dotted line, Liss and Merlivat (1986). See Table 3 for sources. 30 Properties of Water _ Gas Exchange at the AirWater Interface as the partial pressures of the gas in both the air and water phases, and represented as DC Kspw pa 13 Solubility of Gases Solubility of the major gases in the atmosphere differs by several orders of magnitude. For instance CO2 is much more soluble than CH4. The solubility of most gases is inversely related to temperature. Over the range in temperatures experienced in most water bod- ies, the solubility changes by a factor of 2, and decreases approximately 2% C1 for slightly solu- ble gases. Salinity also influences the solubility of gases. Known as the Setschenow effect, the solubility of gases in seawater are decreased by approximately 20% when compared with fresh water. Table 1 gives the solubilities of several selected gases. The values are given as a Bunsen coefficient, b, which is the volume of gas at standard temperature and pressure (STP), dissolved in a unit volume of solution at the temperature (T; degrees Kelvin) when the total pres- sure and fugacity are 1 atm. The Ostwald solubility coefficient (from eqn. [11]) is related to the Bunsen coefficient by: a b T T0 14 where T0 273.15 K. The solubility coefficient (eqns. [12] and [13]) is Ks a=RT 15 where R is the gas constant (e.g., 0.082057 l atm K1 mol1 ). Diffusion Coefficient As described already, the molecular diffusion of gases across the boundary layer is a controlling factor of gas exchange. Like solubility, the diffusion coefficient is also influenced by temperature and salinity. Over the typical range of temperatures of inland waters, diffusion coefficients increase by a factor of three with temperature. In saltwater, diffusion is decreased by about 5%. Schmidt numbers are a useful means of describing diffusion coefficients because they also relate gas exchange coefficients of different gases (eqn. [6]). Some selected Schmidt numbers can be calculated from Table 2. Because diffusion coefficients are tem- perature dependent and ultimately influence gas exchange coefficients, there is a need to normalize gas transfer coefficients for empirical comparison. Gas exchange coefficients can be normalized to a particular Schmidt number. Often, exchange coeffi- cients are normalized to a Sc 600, which is the Schmidt number of CO2 at 20 C in fresh water or to a Sc 660, the Schmidt number of CO2 at 20 C in seawater. The gas exchange coefficient of a particular gas, x (kx), at a Schmidt number of 600 (k600) is k600 kx 600 Scx n 16 Chemical Enhancement Chemical reaction of gases with water can lead to deviations from expected gas transfer relationships. Perhaps the most notable case is for CO2, which undergoes hydration when dissolved in water via two reactions CO2 H2O H2CO3 17 and CO2 OH HCO 3 18 The first reaction is relatively slow and does not influence gas transfer rates significantly. However, the reaction with hydroxide ions is fast, and causes the Table 1 Temperature and salinity dependence of the Bunsen solubility coefficient (b) using the fit to the equation ln b A1 A2(100/T) A3 ln (T/100) S[B1 B2(T/100) B3(T/100)2 ], where T is temperature in degrees Kelvin, and S is salinity in per mille (See the text for conversion between b, a and Ks) Gas A1 A2 A3 B1 B2 B3 O2 58.3877 85.8079 23.8439 0.034892 0.015568 0.0019387 CH4 68.8862 101.4956 28.7314 0.076146 0.04397 0.0068672 CO2 a 60.2409 93.4517 23.3585 0.023517 0.023656 0.0047036 N2 59.6274 85.7661 24.3696 0.05158 0.026329 0.0037252 SF6 520.606 250.6 (75.701)b 0.0117 Abstracted from Wanninkhof R (1992) Relationship between wind speed and gas exchange over the ocean. Journal of Geophysical Research 97: 73737382. The reader is urged to consult and cite the original publication and references therein. a The solubility of CO2 is expressed as Ks instead of a Bunsen solubility coefficient. b For SF6 the term for A3 in the Bunsen coefficient equation is A3 ln(T), rather than A3 ln(T/100). Properties of Water _ Gas Exchange at the AirWater Interface 31 concentration gradient in the boundary layer to increase (Figure 1d), thus enhancing gas transfer. The reaction with hydroxide becomes more impor- tant at high pH. One example where chemical enhancement can be important is in eutrophic sys- tems. The high productivity causes a decrease in CO2 which leads to an increase in pH. Chemical enhancement is also most pronounced at low wind speeds. At higher wind speeds and increased turbu- lence, the chemical reaction no longer becomes rate limiting and physical processes dominate the rate of gas transfer. The chemical enhancement of CO2 also has important implications when considering stable isotope dynamics, as a large isotopic frac- tionation takes place under conditions of chemical enhancement. Other Factors Meteorological Conditions Thermal conditions at the airwater interface influ- ence gas transfer in several ways. Heat can be lost from the surface of the water by several mechanisms including, evaporation, sensible heat loss and long wave radiation. As this heat is lost, the surface layer becomes cooler and convection occurs, due to the buoyant forces of the warmer, less dense water below. This penetrative convection contributes another term to the turbulence in the water column. Including this component of the turbulence regime in lakes aids in the understanding of why gas exchange rates may remain relatively high, even at low wind speeds (see Empirical models of gas exchange, below). Also related to heat loss from the surface is the presence of a cool skin in the top $1 mm of water. This cool skin alters the solubility of gas in the bound- ary layer and results in a different concentration gradient than would be estimated from a measure- ment some distance below. The temperature dif- ference is small, and this factor is probably most important when considering fluxes over large areas, such that small bias could lead to large errors. Surfactants Organic compounds are found on the surface of all natural waters. Generally, surface slicks reduce gas exchange, sometimes significantly. Occasionally they can be found in amounts that require a third layer to be considered when examining gas exchange. Under most conditions, however, they act to change the hydrodynamic conditions of the airwater interface. The presence of surfactants has been shown to reduce wind stress, and also to dampen waves. The role of surfactants is most pronounced at low wind speeds, since at high speeds wave action will distribute the organic compounds throughout the water column, reducing their impact on surface properties. Bubbles The formation of bubbles, usually caused by the breaking of waves, can have a significant impact on gas transfer by enhancing gas exchange. A positive relationship exists between the gas exchange coeffi- cient and the fractional area of bubble plumes caused by whitecapping waves. The most obvious impact of bubbles might be an increased surface area of gas exchange, yet this has been shown to account for only a small percentage of the enhanced gas exchange. Also important is the change in in- ternal pressure of a bubble due to the vertical dis- placement it experiences. This increased pressure effectively alters the DC from what would be experi- enced at the surface. Table 2 Schmidt number relationship with temperature (030 C) for fresh water and seawater (35%): Sc A Bt Ct2 Dt3 , with t in degrees Celsius Gas A B C D O2 (fresh) 1800.6 120.1 3.7818 0.047608 (seawater) 1953.4 128 3.9918 0.050091 CH4 1897.8 114.28 3.2902 0.039061 2039.2 120.31 3.4209 0.040437 CO2 1911.1 118.11 3.4527 0.04132 2073.1 125.62 3.6276 0.043219 N2 1970.7 131.45 4.139 0.052106 2206.1 144.86 4.5413 0.056988 SF6 3255.3 217.13 6.837 0.08607 3531.6 231.4 7.2168 0.090558 The top line for each gas is the freshwater value. Abstracted from Wanninkhof R (1992) Relationship between wind speed and gas exchange over the ocean. Journal of Geophysical Research 97: 73737382. The reader is urged to consult and cite the original publication and references therein. 32 Properties of Water _ Gas Exchange at the AirWater Interface Methods for Estimating Gas Exchange Rates Purposefully Released Tracers Several types of volatile tracers can be used to exam- ine gas exchange. The key aspect of the tracer is that it can be measured with high precision at low concentrations, and remains relatively conservative with regards to other processes besides atmospheric exchange. Perhaps the most useful tracer employed to this point has been sulfur hexafluoride, SF6. The background concentration of this human-made tracer is low and the detection limit is several-fold lower than ambient concentrations. In addition, SF6 is inert. Other easily manageable volatile tracers included propane, ethane, and methyl chloride. However, these tracers are not as stable as SF6. Stud- ies using any of these types of tracers can constrain gas exchange on scales ranging from 0.5 days to several days. Greater precision is gained by measur- ing the concentration change over longer time peri- ods. But, the power to mechanistically explain the drivers of gas exchange is diminished at longer time scales. By injecting a volatile tracer into a water body and following the change in concentration gradient through time it is possible to estimate the gas exchange coefficient. In eqn. [2], F can be replaced by: F @M @t 1 A @Cw @t h 19 where M is the mass of the tracer, A is the area of the flux and h is the average depth of the volume (V) of water that is exchanging with the atmosphere (h V/A). Equation 2, then yields: k @Cw @t h DC ; 20 which after rearranging and integration from the initial to final time (subscripts i and f, respectively) results in, k ln DCi DCf h tf ti 21 For a tracer such as SF6, where aCa < < Cw, the concentration gradient can be approximated by DC Cw. The technique of deliberate volatile tracer addi- tions is particularly suited for small lakes. For larger bodies of water, or where advection is of concern, the use of dual tracers is required. With the dual tracer method, two tracers are added, one being the volatile tracer. The second tracer can either be a nonvolatile tracer or another volatile tracer with differing diffu- sivities. Using a second volatile tracer also requires that the relative rates of exchange between the two tracers be known. With the dual tracers, concentra- tion changes due to dilution can be factored out to ultimately estimate gas exchange. Some nonvolatile tracers include salts, dyes, and bacterial spores. Chambers and Enclosures Floating chambers can be deployed on the surface of the water, and changing headspace concentrations within the chamber used to estimate gas exchange. Naturally present or tracer gases can be measured, and depending on the rate of concentration change, periods as short as several hours can be examined. Thus, it is possible to directly measure the flux of a particular gas, as opposed to estimating it from another tracer gas and Schmidt number relationship. The analysis of the time series of concentrations in the headspace is done in the same way as the tracer analysis and the equation for gas exchange is: k hH atf ti ln DCi DCf 22 where hH is the average height of the chamber above the water. One noted drawback of the chamber method is that the chamber itself may alter the ambient conditions at the airwater interface. The chamber may reduce turbulence (e.g., reducing wind stress), alter the pres- sure (e.g., bobbing motions), or cause an unnatural atmosphere (e.g., increased water vapor). However, when a relative comparison of exchange among two or more gases is of interest, the chambers may prove to be very useful. One example is calculating the enhancement of CO2 flux under conditions of high pH. By measuring CO2 and a nonreactive gas such as methane, and examining the ratios of their exchange coefficients (an indicator of enhancement), most biases imparted by the chamber should be eliminated. Enclosures within the water column can also be employed to estimate gas exchange. Gas concentration can be altered or tracers added to examine the response time of the concentrations to return to equilibrium. Alternately for biologically active gases, chambers excluded from the atmosphere can be monitored con- gruently with the bulk water concentrations. The dif- ference between the two concentration time-series can be attributed to gas exchange with the atmosphere. As with the chamber method, the influence of the apparatus on the results needs to be considered. Eddy Correlation Methods Eddy correlation (covariance) methods directly esti- mate the flux of gas above water surfaces by measur- ing the fluctuations of the vertical wind speed and gas Properties of Water _ Gas Exchange at the AirWater Interface 33 concentrations at a fixed point. The velocity fluctua- tions are represented by v0 v v, where v is the instantaneous vertical velocity and v is the mean. Concentration fluctuations are represented likewise. For demonstration, if CO2 is evading the surface of a lake, there will be a concentration profile of CO2 going from high near the lakes surface to low some distance above the lake surface. An upward fluctua- tion from the mean vertical velocity (positive v0 ) will result in a positive concentration fluctuation (positive C0 ) at the point of measurement, and the instanta- neous flux from lake to air will be positive F v0 C0 . Inversely, a downward fluctuation in vertical velocity (negative v0 ) will result in a negative concentration fluctuation (negative C0 ), also resulting in a positive flux. Therefore, the overall flux is obtained as the correlation of the vertical velocity fluctuations and the concentration fluctuations: F v0C0 23 This method is used extensively in terrestrial ecosys- tems, and appears that it may have utility in aquatic ecosystem also, but application to this point is sparse. Eddy flux measurements require basic meteorological instruments, the most important being a sonic anemom- eter which can resolve wind speeds in three dimensions. In addition, some means of measuring gas concentra- tions at high frequency is required. Often an infra-red gas analyzer is used for appropriate gases. Empirical Models of Gas Exchange Most studies which have derived models for esti- mating gas exchange coefficients have used tracer injections of SF6, and have relied on wind velocity measurements as the predictor variable. Wind veloc- ity has dominated in the study of gas exchange because it is probably one of the more important factors leading to turbulence at the airwater inter- face. Also, wind is relatively easy to measure. The convention for reporting wind speed measurements is for wind speeds at a 10 m height above the water surface. In practice, wind speeds are rarely measured at this height, and instead are calculated based on a logarithmic wind profile. For the measurement of wind speed at a height of x meters (Ux), the wind speed at a height of 10 m (U10) is U10 Ux 1 Cd0:5 k ln 10 x " # 24 where k is the Van Karman constant (0.4) and Cd is the drag coefficient at a height of 10 m. The value for Cd typically ranges from 1.1 103 to 1.5 103 . Table 3 lists several gas exchange coefficient rela- tionships, which have been derived from experiments carried out on lakes of different sizes. Considerable uncertainty in actual rates of gas exchange and appro- priate representation of wind velocities (average vs. instantaneous) has led to disparity among the models (Figure 2). At low wind velocity there seems to be little dependence of gas exchange on wind speeds. At higher velocities, gas exchange rates increase rapidly as a function of wind speed. A notable difference between these models is the intercept at zero wind speed. Because other sources of energy can cause turbulence it seems unlikely that gas exchange rates should decrease to zero. Therefore, other models which take into account other important sources of Table 3 Models of k600 as a function of wind speed. The reader is urged to consult the original publications for descriptions of the wind speed over which the relationships are valid K600 (cm hour1 ) Wind speed (U10) Source k 0.45U10 1.64 1 k 2.07 0.215U10 1.7 2 k 0.72U10 U10 < 3.7 m s1 3 k 4.33U10 13.3 U10 ! 3.7 m s1 k 0.168 0.228U10 2.2 3 k 1 U10 < 3.7 m s1 3 k 5.14U10 17.9 U10 ! 3.7 m s1 k 0.17U10 U10 3.6 m s1 4 k 2.85U10 9.65 3.6 m s1 < U10 13 m s1 K 5.9U10 49.3 U10 > 13 m s1 Sources 1. Wanninkhof R (1992) Relationship between wind speed and gas exchange over the ocean. Journal of Geophysical Research 97: 73737382. 2. Cole JJ and Caraco NF (1998) Atmospheric exchange of carbon dioxide in a low-wind oligotrophic lake measured by the addition of SF6. Limnology and Oceanography 43: 647656. 3. Crusius J and Wanninkhof R (2003) Gas transfer velocities measured at low wind speed over a lake. Limnology and Oceanography 48: 10101017. 4. Liss PS and Merlivat L (1986) Airsea gas exchange rates: Introduction and synthesis. In: Buat-Menard PE (ed.) The role of airsea exchange in geochemical cycling. pp 113127. Boston, MA: Reidel. 34 Properties of Water _ Gas Exchange at the AirWater Interface turbulence, such as penetrative convection, should be considered essential in future research. This is why parameterizing the surface renewal model has become a recent focus. Other Important Aspects of Gas Exchange Three additional aspects of gas exchange in aquatic environments that have received less attention than gas exchange in lakes include gas exchange in streams, rivers and estuaries, macrophyte-mediated gas transfer, and ebullition of gases from sediments. Excellent work has been conducted in these addi- tional disciplines; however, gas exchange remains less constrained in these systems. This lack of con- straint is in a large part due to the variability that can exist within each of these types of environments. Because of the variability, it is often difficult to apply previously derived models from other systems, and parameterizing gas exchange for individual stud- ies is often required. Gas exchange in lotic systems is given as a reaera- tion rate, which is the gas transfer velocity divided by the mean depth of the stream, and these are normalized to oxygen exchange at 20 C. As in lakes, turbulence is key component of gas exchange. Turbulence in lotic systems is complicated by the interaction of the water column with the bottom surface. Factors that are often considered important for gas exchange in flowing waters include: slope, discharge, velocity, width, depth, energy dissipation, roughness, shear velocity, Froude number and Rey- nolds number. Models usually include a subset of these parameters, and not all the parameters listed are independent of one another. The simplest models typically estimate reaeration as: kO2 aUb wHc w 25 where Uw is the water velocity, Hw is the mean depth and a, b, and c are fitted parameters. Models that give satisfactory prediction among systems have been diffi- cult to create. Even within a system extrapolation may be difficult. For instance in a stream, gas exchange will vary considerably between pool and riffle sections. In high gradient streams, bubble entrainment can signifi- cantly alter gas exchange and will vary depending on discharge. Emergent macrophytes can exhibit significant con- trol on the flux of gases in aquatic ecosystems. The movement of gas is of significant importance for aquatic plants, since their roots are often located in sediments that are depleted in oxygen. Therefore sig- nificant amounts of gases are moved between the atmosphere and the rooting zone. Oxygen is supplied to the roots from the atmosphere, and in exchange, other gases can be transported from the sediment to the atmosphere. Emergent macrophytes typically have hollow or pithy spaces that facilitate gas move- ment. Gas can move through these areas by passive diffusion or they can be moved actively by several mechanisms. As O2 is consumed by roots, CO2 is produced and subsequently dissolved in the water. The dissolution in pore waters creates a pressure gradient that causes gases to flow towards the roots. However, sediments are often rich in CO2 and this mechanism is not always important, and may even cause gas to flow from the roots to the atmosphere. Emergent macrophytes can also create a pressurized system through thermal osmosis and the evaporation of water. Macrophytes significantly influence the transport of CH4 and S containing gases. Chambers are the most highly used method for quantifying the role of macrophytes in gas exchange. Care must be exercised to ensure that the chamber does not signifi- cantly alter the thermal or light regime of the plants, since these factors are key components to the plants ability to transport gases. Ebullition (bubble transport) is especially impor- tant in sediments that generate significant quantities of CH4. Methane is only sparingly soluble in water. If the production rate of CH4 is low, most of it will escape the sediments via diffusion. However, if pro- duction rates exceed the diffusion rate, concentra- tions of CH4 will increase to the point that bubbles will form. Bubbles do not instantly release from the sediments, but often require some sort of disturbance. The disturbance can be a change in atmospheric or hydrostatic pressure, temperature, or some other sort of physical disturbance. When bubbles rise through the sediments, they can strip other gases as well. Ebul- lition is usually measured by using inverted funnel- shaped traps, which capture bubbles so that they can be sampled for volume and chemistry. Since physical disturbance is important for ebullition, it is critical that the design of the trap allow for sampling that will not actually be the cause of bubble release. Conclusion From the earlier-mentioned text, one should be able to make rough estimates of gas exchange for many lake settings. A general idea about wind speeds allow for an estimate of k600. Applying the Schmidt number depen- dence permits the calculation of k for the gas of interest. Chemical gradients could be estimated from previous studies or be measured manually. Some temporal vari- ation can be expected for both the gas exchange coeffi- cient and chemical gradients. Nonetheless, a general Properties of Water _ Gas Exchange at the AirWater Interface 35 idea about the magnitude of the flux could be deduced quite easily. Methods of direct measurement are most important in systems (e.g., streams and wetlands) in which empirically derived predictive models are not always applicable. See also: Chemical Properties of Water; Density Stratification and Stability; Dissolved CO2; Gas Exchange at the Air-Water Interface; Methane; Nitrogen; Physical Properties of Water; Pollution of Aquatic Ecosystems I; Pollution of Aquatic Ecosystems II: Hydrocarbons, Synthetic Organics, Radionuclides, Heavy Metals, Acids, and Thermal Pollution; Redox Potential; Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes. Further Reading Anderson DA, Striegl RG, Stannard DI, et al. (1999) Estimating lake-atmosphere CO2 exchange. Limnology and Oceanography 44: 9881001. Bade DL and Cole JJ (2006) Impact of chemically enhanced diffu- sion on dissolved inorganic carbon stable isotopes in a fertilized lake. Journal of Geophysical Research-Oceans 111: C01014. Brustaert W and Jirka GH (eds.) (1984) Gas transfer at water surfaces. Dordrecht: Reidel. Chanton JP and Whiting GJ (1995) Trace gas exchange in fresh- water and coastal marine environments: ebullition and transport by plants. In: Matson PA and Harris RC (eds.) Biogenic Trace Gases: Measuring Emissions from Soil and Water, pp. 98125. Oxford, UK: Blackwell. Donelan MA (1990) Airsea interaction. In: LeMehaute B and Hanes D (eds.) The Sea: Ocean Engineering Science, no. 9, pp. 239292. New York: Wiley. Donelan MA, Drennan WM, Saltzman EM, and Wanninkhof R (eds.) (2002) Gas Transfer at Water Surfaces. (Geophysical Mono- graph 127) Washington, DC: American Geophysical Union. Frost T and Upstill-Goddard RC (1999) Airsea gas exchange into the millennium: Progress and uncertainties. Oceanography and Marine Biology: An Annual Review 37: 1245. Jahne B and Hauecker H (1998) Airwater gas exchange. Annual Review of Fluid Mechanics 30: 443468. Jahne B, Munnich KO, Bosinger R, et al. (1987) On the parameters influencing airwater gas exchange. Journal of Geophysical Research 92: 19371949. MacIntyre S, Wanninkhof R, and Chanton JP (1995) Trace gas exchange across the airwater interface in freshwaters and coastal marine environments. In: Matson PA and Harris RC (eds.) Biogenic Trace Gases: Measuring Emissions from Soil and Water, pp. 5297. Oxford, UK: Blackwell. Melching CS and Flores HE (1999) Reaeration equations derived from U.S. Geological Survey database. Journal of Environmental Engineering 125: 407414. Wanninkhof R (1992) Relationship between wind speed and gas exchange over the ocean. Journal of Geophysical Research 97: 73737382. 36 Properties of Water _ Gas Exchange at the AirWater Interface Light, Photolytic Reactivity and Chemical Products A V Va hatalo, University of Helsinki, Helsinki, Finland 2009 Elsevier Inc. All rights reserved. Photochemistry Starts from the Absorption of Solar Radiation Photochemical reactions of organic matter can take place in surface waters and any irradiated surfaces of organic or inorganic substrata. The prerequisite for photochemical reactions is the absorption of radia- tion. The photolytic ultraviolet (UV) and short wave- length visible radiation ($290500 nm) is primarily responsible for abiotic photochemical reactions. In many surface waters, chromophoric dissolved organic matter (CDOM) dominates the absorption of photo- lytic solar radiation. In strict sense, CDOM is an optical definition for dissolved organic matter res- ponsible for the absorption of solar radiation, but in this article CDOM is also treated as a representative organic matter having characteristics similar to humic substances. Primary Photophysics and Subsequent Secondary Chemical Reactions During absorption, a photon (hn) delivers its energy (250400 kJ mol1 at 280500 nm) to the absorber molecule and excites the molecule from its ground state (S0) to the first excited electronic singlet state (S1); CDOM(S0) hn ! CDOM(S1). Excited CDOM releases its excitation energy mostly as heat (with 0.950.98 probability) but also as fluorescence (prob- ability of $0.01; CDOM(S1) ! CDOM(S0) hn) at the nanosecond time scale. The excited singlet state of CDOM may be converted into an excited triplet state (T1, probability of 0.010.04; CDOM (S1) ! CDOM(T1)). The excited triplet state of CDOM has greater than microsecond-lifetime and may undergo secondary (thermal) chemical reactions, but it can also transfer its excitation energy to another compound or release it as heat or a photon (phosphorescence). Numerousreactionpathwaysare availableforexcited states (e.g., homolysis of bonds, heterolysis, ionization, intermolecular oligomerization, intramolecular rearran- gements, and photoisomerization). Because the energy of photon can be larger than the dissociation energy of chemical bonds, the excited molecules may dissociate (probability of 105 ) or ionize CDOM (e.g., CDOM hn ! CDOM e (aq); probability of 103 104 ). The fragmentation may take place via homolysis or heterolysis of d- and p-bonds, e.g., next to the carbonyl functional groups of CDOM (e.g., type I and II Norrish reactions). The fragmentation of excited molecules results in radical species (such as organoperoxy radi- cals), which further can lead to the expulsion of carbon monoxide, carbon dioxide, or other small molecules. The excited CDOM (triplet states in particular) can transfer their excitation energy to other molecules (often called a quencher). Dissolved dioxygen is a common acceptor of this energy. Energy transfer to O2 generates reactive oxygen species (singlet oxygen, 1 O2; superoxide, O2 ; hydroxyl radicals. OH and hydrogen peroxide, H2O2) and is seen as the photo- chemical consumption of O2. Hydroxyl radical is the most reactive oxygen species and can react effectively with organic and inorganic matter as well as cell con- stituents of organisms. In surface waters, the lifetime of H2O2 can be greater than several hours, while those of 1 O2, O2 , and OH are much lower than a second. The photochemical formation of reactive oxygen species can proceed also via photolysis of nitrate and nitrite as well as via photo-Fenton reaction involving iron. The photochemical reactions concerning the pri- mary absorber are frequently called direct photo- chemical reactions. A direct photoreaction takes place, e.g., when CDOM absorbs solar radiation and becomes photochemically transformed. An example is the photobleaching of CDOM, when photochemistry decreases the absorption of CDOM. If photochemical reactions concern other molecules than the primary absorber, they are called indirect photochemical reac- tions and the primary absorber is called a sensitizer. The indirect photochemistry may concern molecules that cannot absorb solar radiation themselves but react with, e.g., the photochemically generated reactive oxy- gen species. For example, algal-derived DOM is largely transparent to solar radiation and cannot be directly photochemically transformed alone. In the presence of CDOM sensitizer, solar radiation can transform algal DOM into a biologically recalcitrant form. Photochemistry of Organic Carbon In many fresh waters, the majority (5090%) of DOM consists of heterogeneous high molecular weight (>1000 g mol1 ) colored humic substances (CDOM), which are sensitive to photochemical decomposi- tion sensitive to direct photochemical decomposition. Large molecular mass, heterogeneous structure, and nonhydrolyzable bonds make CDOM recalcitrant against biological metabolism in the water column. 37 OH O HO O OH O O HO OH O HO O OH O HO O OH O HO O OH O HO O OH O HO O OH O HO OHO O OH OH OO HO OH O HO O OH O OHO HO OH O OH O OH O HO OH O O OH O O OH OH O OHHO O OH O OH O O OHHO OH OO OH O O OH O OH O HO HO O HO HO OH CO O C CH2 O O O O O O O NH4 + N OO N O OH N O O OH N O N N OH N O O O OH N O OH N O N 17 11 161514 131210 18 19 20 2221 23 24 22 25 26 27 28 29 30 31 32 3433 37 42 43 44 41 OH O O 1 2 3 4 5 6 7 8 9 38 39 40 35 36 O C C Figure 1 Identified photoproducts of irradiated natural dissolved organic matter. The most abundant products are marked with bold. (1) carbon dioxide; (2) carbon monoxide; (3) formaldehyde; (4) ethene; (5) acetaldehyde; (6) glyoxal; (7) acetone; (8) methyl glyoxal; (9) propene. Monocarboxylic acids: (10) formic acid; (11) acetic acid; (12) glycolic acid; (13) glyoxylic acid; (14) propionic acid; (15) lactic acid; (16) 3-hydroxy propanoic acid; (17) 3-hydroxy 2-propenoic acid; (18) pyruvic acid; (19) butanoic acid; (20) 3-oxobutanoic acid; (21) levulinic acid; (22) hexanoic acid; (23) hexadecanoic acid; (24) octadecanoic acid; (25) 2-hydroxy benzoic acid; (26) 2,4-dihydroxy benzoic acid. Di-tricarboxylic acids: (27) oxalic acid; (28) malonic acid; (29) fumaric acid; (30) succinic acid; (31) methylene succinic acid; (32) methyl succinic acid; (33) malic acid; (34) methyl malic acid; (35) pentane dioic acid; (36) terephtalic acid; (37) citric acid. N containing products: (38) ammonium; (39) nitrite; (40) glycine; (41) serine; (42) histidine; (43) glutamic acid; (44) citrulline. Kieber RJ, Zhou X, and Mopper K (1990) Formation of carbonyl compounds from UV-induced photodegradation of humic substances in natural waters: Fate of riverine carbon in the sea. Limnology and Oceanography 35: 15031515. Mopper K, Zhou X, Kieber RJ, et al. (1991). 38 Properties of Water _ Light, Photolytic Reactivity and Chemical Products Because the biologically recalcitrant CDOM is photo- chemically reactive, the photochemical transformation of CDOM and photooxidation of nonhydrolysable bonds of CDOM are major photoreactions in lakes. The most abundant identified photochemical prod- uct of natural CDOM is carbon dioxide (CO2) or, more correctly, inorganic carbon existing as CO2, H2CO3, HCO3 , or CO3 2- depending on pH (Figure 1). Photochemical reactions produce low molecular mass organic compounds from CDOM (Figure 1). Identified products include carboxylic acids (33 of those in Figure 1), few carbonyl compounds, volatile alkenes, and carbon monoxide. When the photo- chemical production of CO and CO2 has been deter- mined from the same waters, the photoproduction rate of CO has been 57% of that of CO2. The magnitude of four photoproduced carboxylic acids (formic, acetic, oxalic, and malonic acid) has corre- sponded to 3050% (mean 34%) of the photo- produced CO2 in 38 Swedish lakes and also in other fresh waters. Most of the identified organic photoproducts of CDOM (Figure 1) are directly bioavailable for bac- terioplankton, and are called biologically available photoproducts (BAPs). The total magnitude of BAPs is quantified by measuring bacterial carbon consump- tion, which is caused by the irradiation of CDOM. For example, bacteria assimilated BAPs at a magnitude similar to the photoproduction of CO2 during the irradiation of humic lake water (Lake Valkea-Kotinen, Finland) when cultured in the irradiated water after the irradiation. Solar radiation mineralized 27 mmol carbon per liter of Parker River DOM (USA) into CO2 but produced 54mmol carbon per liter BAPs. According to those studies, the amount of BAPs can be nearly similar to or twofold larger than the photo- production of CO2. Thus, in addition to the direct photochemical mineralization of CDOM, a combined action of photochemistry and microbial respiration based on BAPs leads to the mineralization of organic carbon. Photochemical reactions decompose the aromatic moieties of CDOM and typically decrease the molecu- lar mass of CDOM. The decrease in aromaticity, in molecular mass and changes in the functional groups change the chemical and physical properties of CDOM. Photochemical reactions increase the water solubility of humic acids, decrease the light absorption of CDOM, decrease the sorption of CDOM towards surfaces or hydrophobic organic chemicals, and change the composition of functional groups (ligands) respon- sible for the chelating of metals. Photochemical reac- tions can also increase molecular mass of CDOM and even precipitate it. However, further irradiation of photochemically formed high molecular mass CDOM eventually result in low molecular weight compounds. Solar radiation decomposes the fluorophores and light absorbing moieties of CDOM in a process called photobleaching. An extensive photobleaching requires the presence of O2. The photochemical loss of car- bonyl chromophores into low molecular weight organic compounds, and the destruction of aromatic and quinone structures of CDOM are likely responsi- ble for the photobleaching. Under extensive expo- sures to solar radiation, photochemical reactions can destroy completely the chromophores and fluor- ophores of organic matter. The photobleaching of CDOM takes place faster than the mineralization of dissolved organic carbon (DOC), and after complete photochemical loss there will be some nonchromo- phoric DOC left. Experimental and modeling studies suggest that solar radiation-induced photobleaching is primarily responsible for the total decomposition of CDOM in surface waters, and contributes remark- ably to the observed in-lake losses of the imported CDOM. Because CDOM is largely responsible for the absorption of UV radiation and low wavelength visi- ble radiation, photobleaching increases penetration of solar radiation into the water column, and thus inter- feres with the UV radiation exposure of organisms, the light availability of photosynthetic organisms, and the thermal stratification of the water column. Photochemical degradation of dissolved organic carbon and its impact on the oceanic carbon cycle. Nature 33: 6062. Backlund P (1992). Degradation of aquatic humic material by ultraviolet light. Chemosphere 35: 18691878. Allard B, Bore n H, Pettersson C, and Zhang G (1994) Degradation of humic substances by UV irradiation. Environment International 20: 97101. Wetzel RG, Hatcher PG, and Bianchi TS (1995) Natural photolysis by ultraviolet irradiance of recalcitrant dissolved organic matter to simple substrates for rapid bacterial metabolism. Limnology and Oceanography 40: 13691380. Corin N, Backlund P, and Kulovaara M (1996) Degradation products formed during UV-irradiation of humic waters. Chemosphere 33: 245255. Kulovaara M, Corin N, Backlund P, and Tervo J (1996) Impact of UV254-radiation on aquatic humic substances. Chemosphere 33: 783790. Bertilsson S and Tranvik L (1998) Photochemically produced carboxylic acids as substrates for freshwater bacterioplankton. Limnology and Oceanography 43: 885895. Riemer DD, Milne PJ, Zika RG, and Pos WH (2000) Photoproduction of nonmethane hydrocarbons (NMHCs) in seawater. Marine Chemistry 71: 177198. Tarr MA, Wang W, Bianchi TS, and Engelhapt E (2001) Mechanisms of ammonia and amino acid photoproduction from aquatic humic and colloidal matter. Water Research 35: 36883696. Kieber RJ, Li A, and Seaton PJ (1999) Production of nitrite from the photodegradation of dissolved organic matter in natural waters. Environmental Science and Technology 33: 993998. Shiller AM, Duan S, van Erp P, and Bianchi TS (2006) Photo-oxidation of dissolved organic matter in river water and its effect on trace element speciation. Limnology and Oceanography 51: 17161728. Properties of Water _ Light, Photolytic Reactivity and Chemical Products 39 Photochemistry of Nitrogen Photochemical reactions can release ammonium (NH4 ) from dissolved organic nitrogen (DON) when the concentration of DON is high and that of NH4 low (8 mM) or NH3, photochemical reactions can also incorporate these inorganic N-species into DON. In addition, photochemical reactions can convert aro- matic amino acid (tryptophan) and protein (in the presence of CDOM) into less bioavailable forms. Photochemistry of Phosphorus Ferric (Fe3 ) iron binds phosphate ion tightly and can associate with organic matter to form Fe(III)Pi CDOM complexes. Photochemical reactions can release phosphate (PO4 3 ) from ferric ironphosphorushumic complexes (Fe(III)PiCDOM). The phosphorus of these complexes is not readily available for organisms. When these complexes absorb solar radiation, ferric iron (Fe3 ) can be photoreduced into ferrous iron (Fe2 ) and a phosphate ion is released. Unlike many photochemical reactions of natural DOM, the photo- reduction of ferric iron and subsequent release of phosphate can be a very rapid process (half-lives minuteshours). The photochemical release of Pi from the Fe(III)PiCDOM complexes may be an important pathway for converting nonbioavailable P into a bio- available form. Coupling of Photooxidation of Organic Matter to the Photoreduction of Metals Metals can associate with organic matter and can become photoreduced via a ligand-to-metal charge- transfer pathway when exposed to natural solar radiation (Figure 2). When organic matter associates with iron, its absorption and the probability for photochemical transformation increases. Photochem- ical reactions can photoreduce ferric iron to more soluble ferrous iron and at the same time oxidize organic matter, e.g., via decarboxylation reactions, which can lead to the production of inorganic carbon and hydrogen peroxide (H2O2). Ferrous iron (II) is often quickly oxidized to ferric iron (III) in a dark process, which consumes dissolved oxygen or reactive oxygen species. If H2O2 is the oxidizer of Fe(II), the process produces hydroxyl radicals via Fenton reac- tion: Fe(II) H2O2 ! OH Fe(III). When solar radiation produces both Fe(II) and H2O2, this reac- tion is called a photo-Fenton reaction. Heterogeneous Photochemistry Photochemistry can modify particulate organic mat- ter or organic matter adsorbed on the surfaces. The photochemical reactions associated with surfaces are called heterogeneous in contrast to the homogenous photochemistry of dissolved molecules. Heterogeneous photochemical reactions take place on any surfaces exposed to photolytic solar radiation, e.g., on the surfaces of sediment or particles in sus- pension. The photochemical reactions on surfaces of natural mineral particles are largely similar to those in the dissolved phase. Photochemical reduction of iron(III) and dissolution of Fe takes place also on Fe(OH)3-OMred hn e.g., O2; H2O2 Fe(III)aq Fe(OH)3(s) OMox (e.g., CO2 ) OMred Fe(II)aq O2 H+ CO2 Photoreduction Photooxidation O xidation Reduction e.g., O 2consum ption OH production Precipitation Complexation M ineralization H2O2formation Figure 2 Schematic representation of the aquatic photoredox cycling of iron and its coupling to the oxidation of organic matter (OM) in illuminated surface waters. Fe(II)aq dissolved ferrous iron; Fe(III)aq dissolved ferric iron; Fe(OH)3(s) ferric hydroxide; OMred reduced organic matter, which is a ligand for Fe(III); Fe(OH)3OMred a complex between reduced OM and Fe(III); OMox oxidized organic matter; CO2 carboxylic radical. The oxidation of Fe(II) with hydrogen peroxide is called the Fenton reaction (H2O2 Fe(II) ! Fe(III) OH OH ) and it generates hydroxyl radicals. Adapted from Sulzberger B (1992) Heterogeneous photochemistry. In Stumm W (ed.) Chemistry of the SolidWater Interface, pp 337367. New York: John Wiley. 40 Properties of Water _ Light, Photolytic Reactivity and Chemical Products surfaces of colloidal or solid iron minerals. Concomi- tantly with the photoreduction of iron III, organic carbon adsorbed on particles is oxidized and O2 con- sumed. Solar radiation can mineralize and decrease the molecular mass of organic matter adsorbed on the surfaces of mineral (e.g., clay) particles. This process decreases the adsorption of CDOM on surfaces and leads to the dissolution of DOC. Such DOC has larger bioavailability than the organic matter adsorbed on the surfaces of mineral particles. Photochemical reactions also interfere with the decomposition of particulate dead organic matter (detritus) such as senescent phytoplankton or macro- phytes. The (photosynthetic) pigments are primary absorbers of solar radiation and susceptible for pho- tolysis in detrital plants with nonfunctional photo- protective apparatus. The photolysis of pigments in surface waters is an important mechanism for their decomposition, because pigments decompose inef- fectively in dark anaerobic sediments. The lignin of vascular plant detritus is highly suscep- tible for photolysis. The photochemical decomposition of lignin can break down the structural integrity of detrital plant material, enhance the leaching of partic- ulate organic matter into DOM, and induce the loss of particulate organic matter. Photochemical reactions can also directly mineralize detrital plant material into CO2. The exposure of detrital leaves to solar radiation can increase or decrease microbial activity on leaves possibly depending on the diagenetic state and the bioavailability of detrital leaves. Photochemical Reactivity of Organic Matter Photochemical reactivity of organic matter describes the susceptibility of organic matter to photochemical transformation and is quantitatively described by an apparent quantum yield (AQY or f). The AQY for a photochemical reaction describes the magnitude of photochemical reaction (mole of photochemical product) in relation to the magnitude of photons absorbed by the sample (mole of absorbed photons). The variability of AQYs is large among different photochemical reactions (Figure 3). For example, the AQY can be around 1 as is the case for the photochem- ical reduction of ferric iron of ferrioxalate, which can be coupled to the production of CO2 (Figure 3). In this case, every photon absorbed by ferrioxalate reduces ferric iron to ferrous iron. When nitrate absorbs solar radiation, 1 mol of absorbed photons generates 0.017 mol of hydroxyl radicals and nitrogen dioxide. NO 3 hv H ! NO2 OH The AQY for this reaction is 0.017. For known single chemical compounds (as for the nitrate and ferrioxalate above), the AQY is often assumed to be the same through that part of the spectrum, where solar radia- tion and the absorption of the compound interact. This is exemplified as a constant AQY for the photolysis of nitrate at wavelengths c.290345nm (Figure 3). The AQYs for the photochemistry of CDOM are typically low but they vary also a lot and have a strong spectral dependence (Figure 3). The spectral depen- dence likely reflects the heterogeneity of chromophores and the photochemical reactivity of thousands of com- pounds included in CDOM. For example, when AQY was determined for the photochemical formation of CO in three fresh waters of North America, AQY ranged from 0.000 023 to 0.000 068 at 350nm and showed an exponentially decreasing trend with increasing wavelength (Figure 3). Similar exponential spectral dependence has been found for the photo- chemical consumption of O2, the photobleaching of CDOM, the photoproduction of CO2, H2O2, ethene, and OH. Photochemical reactivity of DOM does not always follow exponential spectral dependence. Devia- tion of this behavior has been found in processes where iron has been involved for example for the (photo-) Fenton-type production of hydroxyl radicals. For the most photochemical reactions of CDOM, the magni- tude and spectral dependence of AQY can be described by an exponential equation as illustrated by lines for the photochemical production of CO2, BAPs, and NH4 in Figure 3. One commonly used equation is fl a expbl where fl is the AQY at the wavelength l, a is a pre- exponential factor, and b is a spectral slope coefficient (nm1 ). For example, the AQY spectrum for the photo- chemical mineralization of DOC (fDOC,l) had a 7.52 (mol carbon per mol photons) and b 0.028 (nm1 ) in the water of the humic Lake Valkea-Kotinen. From this equation one can calculate that fDOC,300 1600, fDOC,350 400, fDOC,400 100, and fDOC,450 20mmol carbon (mol photons at l)1 . In other words, 1 mol of photons absorbed by CDOM at 450 nm miner- alizes 20 mmol DOC, while the mole of photons absorbed at 300 nm mineralizes 1600 mmol DOC. By comparing AQYsamong different photochemical reactions, one gets an idea about the relative impor- tance of these photochemical reactions. For example, AQY for the formation of BAPs in Altamaha River (fBAP,350 8 104 ) is much larger than AQYs for the CO photoproduction in three North American fresh waters (fCO,350 2.36.8 105 ) or that for ethene photoproduction in the Parker River water (Florida; fethene,334 6.5 108 ). Thus, photopro- duced CO or ethene contributes only little to the Properties of Water _ Light, Photolytic Reactivity and Chemical Products 41 photoproduction of biologically labile photoproducts. According to AQYs, the reactive oxygen species (OH, H2O2, 1 O2) could potentially contribute in large extent to the photoproduction of CO2. The recent studies, however, suggest that photoproduced OH contributes little (perhaps 88% of solar radiation at 300500 nm (Figure 4(f)). When integrated over wavelengths, the photomineralization rate over the entire water col- umn is 1.1 mmol carbon per square meter per day. Solar Radiation Spectrum Responsible for Photochemical Reactions The solar UV and short wavelength visible part of the spectrum are mostly responsible for photochemical reactions in surface waters (Figure 4(d) and 4(h)). Although the UV-B radiation (290315 nm) is the most energetic part of the solar spectrum reaching surface waters, the irradiance in that range of spectrum is only 0.1% of the global radiation (2903000 nm). Therefore, the less energetic but more abundant UV-A (315400 nm, $6% of global radiation) is often responsible for photochemical reactions. The solar radiation peaks at the visible range of the spectrum (400700 nm covers $50% of global radiation) but at that range of spectrum the energy of photons is lower and much of the radiation is absorbed by particles (e.g., plants) and H2O. Very close to surface, the short wave- length solar UV radiation contributes (e.g., UV-B) most to photoreactions, but as these wavelengths attenuate steeply into water column, longer wavelength radiation (UV-A and visible radiation) becomes more important at deeper depths. Because solar UV-A radiation is often mostly responsible for the photochemical transformation of DOM, the attenuation of solar UV-A radiation into the water column describes roughly also the attenuation of photochemical reactions. The optical characteristic of water column such as the concentration of CDOM, regulate the attenuation of solar UV radiation into water columns. The attenuation of UV-A radiation varies a lot among surface waters. For example, the vertical attenuation coefficient for 380 nm, Kd,380, ranged from 0.07 to 31.7 m1 in 65 American lakes. In these lakes, the calculated depth where the irradi- ance at 380 nm and the photochemical transformation of DOM is 10% of the values at the surface ranges from 0.07 to 33 m. If the solar radiation reaches the solid surfaces such as plant detritus or sediments, much of solar UV radiation and photochemistry attenuates with Kds up to 27 000 m1 into a very narrow (711% of BR) In 1.57.5 m epilimnia of four lakes, Sweden Grane li et al. (1996) 4200(*)(3% of BR) In 50-m water column of Rio Negro-river, Brazil Amon and Benner (1996) 2690(*)(11% of BR) In 1-m epilimnion of Neusiedler See, Germany Reitner et al. (1997) 1000(*)(30% of BR) In 1-m epilimnion of Lake Valkea-Kotinen, Finland Va ha talo et al. (2000) 17002250(*) Lake Skervatjern, Norway Salonen and Va ha talo (1994) 1000(c) Lake Tuscaloosa, AL, USA Va ha talo and Wetzel (2004) 30005000(c) Seven lakes, Canada Molot and Dillon (1997) 1100(c) Parker River estuary Pullin et al. (2004) 4200(c) (20% of BR) Lake O retra sket, whole lake, Sweden Pers et al. (2001) 1280(c) (31% of BR) Annual, Lake Ple sne , whole lake, Czech Republic Kopa c ek et al. (2004) DOC ! BAPs 3800(c) (10% of BCD) In 3.5 m epilimnion of L. Ska rhultsjo n, Sweden Bertilsson and Tranvik (1998) 780(c) (11% of BCD) In 1-m epilimnion of L. Valkea-Kotinen Va ha talo et al. (2003) 1600(c) Parker River estuary Pullin et al. (2004) 9003000(c) Coastal seawater 065 N Miller et al. (2002) 570(c) (up to 20% of BCD) Coastal mean annual Moran and Zepp (1997) DON ! NH 4 2944(c) A coastal lagoon Buffam and McGlathery (2003) 71(c) Humic Lake Valkea-Kotinen Va ha talo et al. (2003) 16102(c) Offshore Baltic Sea Va ha talo and Zepp (2005) 2326(c) Coastal Baltic Sea Va ha talo and Ja rvinen (2007) * Measured; c calculated. BR bacterial respiration biological mineralization of DOC. BCD bacterial carbon demand in the epilimnion. Sources Grane li W, Lindell M, and Tranvik L (1996) Photo-oxidative production of dissolved inorganic carbon in lakes of different humic content. Limnology and Oceanography 41: 698706. Reitner B, Herndl GJ, and Herzig A (1997) Role of ultraviolet-B radiation on photochemical and microbial oxygen consumption in a humic-rich shallow lake. Limnology and Oceanography 42: 950960. Amon RMW and Benner R (1996) Photochemical and microbial consumption of dissolved organic carbon and dissolved oxygen in the Amazon River system. Geochimica et Cosmochimica Acta 60: 17831792. Va ha talo AV, Salkinoja-Salonen M, Taalas P, and Salonen K (2000) Spectrum of the quantum yield for photochemical mineralization of dissolved organic carbon in a humic lake. Limnology and Oceanography 45: 664676. Salonen K and Va ha talo A (1994) Photochemical mineralisation of dissolved organic matter in Lake Skervatjern. Environment International 20: 307312. Va ha talo AV and Wetzel RG (2004) Photochemical and microbial decomposition of chromophoric dissolved organic matter during long (monthsyears) exposures. Marine Chemistry 89: 313326. Molot LA and Dillon PJ (1997) Photolytic regulation of dissolved organic carbon in northern lakes. Global Biogeochemical Cycles 11: 357365. Pullin MJ, Bertilsson S, Goldstone JV, and Voelker BM (2004) Effects of sunlight and hydroxyl radical on dissolved organic matter: Bacterial growth efficiency and photoproduction of carboxylic acids and other substrates. Limnology and Oceanography 49: 20112022. Miller WL, Moran MA, Sheldon WM, Zepp RG, and Opsahl S (2002) Determination of apparent quantum yield spectra for the formation of biologically labile photoproducts. Limnology and Oceanography 47: 343352. Pers C, Rahm L, Jansson A, Bergstro m A.-K, and Janssen M (2001) Modelling dissolved carbon turnover in humic lake O rtra sket, Sweden. Environmental Modeling and Assessment 6: 159172. Kopa c ek J, Braza kova M, Hejzlar J, Nedoma J, Porcal P, and Vrba J (2004) Nutrient cycling in a strongly acidified mesotrophic lake. Limnology and Oceanography 49: 12021213. Bertilsson S and Tranvik LJ (1998) Photochemically produced carboxylic acids as substrates for freshwater bacterioplankton. Limnology and Oceanogra- phy 43: 885895. Va ha talo AV, Salonen K, Mu nster U, Ja rvinen M, and Wetzel RG (2003) Photochemical transformation of allochthonous organic matter provides bioavailable nutrients in a humic lake. Archiv fu r Hydrobiologie 156: 287314. Moran MA and Zepp RG (1997) Role of photoreactions in the formation of biologically labile compounds from dissolved organic matter. Limnology and Oceanography 42: 13071316. Buffam I and McGlathery KJ (2003) Effect of ultraviolet light on dissolved nitrogen transformations in coastal lagoon water. Limnology and Oceanography 48: 723734. Va ha talo AV and Zepp RG (2005) Photochemical mineralization of dissolved organic nitrogen to ammonium in the Baltic Sea. Environmental Science and Technology 39: 69856992. Va ha talo AV and Ja rvinen M (2007) Photochemically produced bioavailable nitrogen from biologically recalcitrant dissolved organic matter stimulates production of nitrogen-limited microbial food web in the Baltic Sea. Limnology and Oceanography 52: 132143. 46 Properties of Water _ Light, Photolytic Reactivity and Chemical Products Two studies have shown that the stimulatory response from the photoproduced carbon substrates can be seen as an increased production of metazooplank- ton (Daphnia). These studies provide evidence that photochemically produced labile substrates can con- tribute to the whole heterotrophic food web of a lake. According to the current limited information, BAPs contribute 1011% of bacterial carbon demand in two lakes (Table 1). One should notice that in both of these lakes, the photolytic stratum was $10% of the depth of epilimnion over which the integration of bacterial carbon demand was made. Thus, one can expect even larger contributions of BAPs to bacterial carbon demand in lakes, where the depths of photo- lytic and mixing stratum are more equal. Several recent studies have indicated that bacterial growth efficiency (BGE produced biomassC/con- sumed DOC) is lower in irradiated water samples than indarkcontrolsamples. Severalfactors may explain this finding. Although BAPs contain bioavailable carbon, their nutrient (N and P) content is low. The oxidation state of carbon is higher in the photoproducts than in bacterial biomass. The bacteria can respond negatively on the exposure to UVradiation and on the detrimental photoproduced H2O2. Additionally, solar radiation can decrease the exoenzymatic activity of bacteria and decrease the utilization of polymeric DOM. The food web gaining from the BAPs can be con- sidered to consist, e.g., from primary producers (I) ! humification of organic matter ! photochemical oxi- dation of organic matter ! bacterioplankton (II) ! flagellates (III) ! ciliates (IV) ! metazooplankton (V) ! fish (VI). This kind of detritus-based food web can contain many trophic levels (e.g., six marked with IVI in the above example, but only up to IV, if metazooplankton consumes bacterioplankton directly) and about 50% respiratory losses of carbon take place at each trophic transfer. As the photochemical oxidation additionally directly mineralizes a large portion of organic carbon to CO2, the trophic effi- ciency of a food web based on photoproduced labile substrates is lower than that of a short herbivory- based food web (e.g., phytoplankton (I) ! metazoo- plankton (II) ! fish (III)). Thus, the gain from BAPs transfers relatively ineffectively to the higher trophic levels of freshwater ecosystems. However, because most (always >50%) of the primary production enters detritus food webs and CDOM is the major source of carbon in many freshwater ecosystems, the detritus-based food webs assisted by the photopro- duction of BAPs can contribute significantly to the productivity of many aquatic ecosystems. Photochemical transformation of organic matter can also decrease the bioavailability of organic matter. This phenomenon has been found out in particular with relatively fresh labile organic matter such as protein-, algal-, or macrophyte-derived organic mat- ter or exudates. Solar radiation can also convert sim- ple unsaturated fatty acids and NH3 into humic substances. This photoreaction does reduce the bio- availability of both carbon (fatty acids) and nitrogen (NH3) substrates. These studies suggest that in eutro- phic lakes with high concentrations of labile organic matter, photoreactions can slow down the turnover time of organic matter by converting biologically labile organic matter into humic-like organic mate- rial. This photochemical formation of humic sub- stances can be seen as a temporary break in the lake metabolism, which allows a part of the bioavailable organic matter to enter into a large pool of biologi- cally recalcitrant organic matter. This kind of humic material can be transported downstream, where it is susceptible for slow biological consumption or pho- tochemical transformation into more bioavailable forms. Thus, in the case of eutrophic lakes, photo- chemical transformation of bioavailable organic mat- ter into less bioavailable humic type of material can be seen as a buffering mechanism, which balances the periods and sites of high production between the sites and the times of low productivity. Photoproduced NH4 can serve as a nutrient for both bacterioplankton and phytoplankton. Although the photochemistry of DOM produces more C-than N-products, the relatively small amount of the latter can have implications for the productivity of plank- ton under N-limiting conditions. Taking into account the low BGE with photoproduced carbon substrates, it has been suggested that the photoproduced NH4 contributes more to bacterial production than photo- producted C-substrates do. Phytoplankton can directly assimilate the photoproduced NH4 or respond indi- rectly to photoproduced NH4 assimilated by bacter- ioplankton. Mixotrophic phytoplankton can graze on bacterioplankton and assimilate N bound in bacterial biomass. Heterotrophic grazers (flagellates and ciliates) retain a portion of the ingested particulate nitrogen in their biomass, while a portion becomes mineralized and can supply inorganic nitrogen for autotrophic primary producers. Thus the photochemical transfor- mation of DOM can contribute to both heterotrophic and autotrophic production in surface waters. Contribution of Photochemistry to the Biogeochemistry of Organic Matter Photochemical decomposition of biologically recalci- trant but photochemically reactive organic matter has importance also at a landscape perspective. A part of the productivity in terrestrial ecosystems and Properties of Water _ Light, Photolytic Reactivity and Chemical Products 47 wetlands is converted into CDOM, which is decom- posed extremely slowly (turnover times of up to 1001000 years) in dark waterlogged anaerobic soils. When such soils are hydrologically connected to sur- face waters, the imported allochthonous CDOM is exposed to solar radiation and becomes photochemi- cally decomposed. The photochemical decomposition can remarkably accelerate the turnover of CDOM derived from terrestrial or wetland sources. For exam- ple, photochemical reactions mineralized 20% of introduced synthetic lignin mixed in humic lake water during a week-long exposure to surface solar radiation while no microbial mineralization of synthetic lignin was detected during the same time in darkness. In another example, the half-life of CDOM from Lake Tuscaloosa reservoir was 1 week under surface solar radiation but $70 weeks in the presence of heterotro- phic microbes in darkness. The photolytic half-lives of allochthonous CDOM in mixing stratum of lakes can be 1001000 times faster than the turnover time of organic matter in soils of terrestrial and wetland ecosystems. Molot and Dillon (1997) cal- culated that the photooxidation of DOC to CO2 was potentially fully responsible for the in-lake losses of inflowing allochthonous DOC in seven Canadian lakes (Figure 5). Their calculations suggest that photolytic decomposition is a primary mechanism for the removal of biologically recalcitrant but photochemically reactive CDOM in lakes. The photochemical mineralization of CDOM may thus convert allochthonous CDOM into CO2 and contribute to the supersaturation of CO2 and the transport of CO2 from lake to atmosphere. See also: Carbon, Unifying Currency; Gas Exchange at the Air-Water Interface; Interactions of Dissolved Organic Matter and Humic Substances; Iron and Manganese; Nitrogen; Organic Nitrogen; Phosphorus. Further Reading Blough NVand Zepp RG (1995) Reactive oxygen species in natural waters. In: Foote CS, Valentine JS, Greenberg A, and Liebman JF (eds.) Active Oxygen in Chemistry, pp. 280333. London: Blackie Academic. Bushaw KL, Zepp RG, and Tarr MA (1996) Photochemical release of biologically available nitrogen from aquatic dissolved organic matter. Nature 381: 404407. Caesar D, Graneli W, Kritzberg ES, and Anesio AM (2006) Stimu- lation of metazooplankton by photochemically modified dissolved organic matter. Limnology and Oceanography 51: 101108. Kieber RJ, Hydro LH, and Seaton PJ (1997) Photooxidation of triglycerides and fatty acids in seawater: Implication toward the formation of marine humic substances. Limnology and Ocean- ography 42: 14541462. Mopper K and Kieber DJ (2002) Photochemistry and the cycling of carbon, sulfur, nitrogen and phosphorus. In: Hansell DA and Carlson CA (eds.) Biogeochemistry of Marine Dissolved Organic Matter, pp. 456507. San Diego: Academic Press. Bact Phytopl Cil zpl Flag Alloc DOC DOC CO2 Microbial link Microbial loop Photooxidation Grazing Autoc DOC Inflow Outflow Production ofCDO M Figure 5 Schematic representation of the carbon cycling in a lake pelagial. The figure emphasizes the role of photooxidation as a major mineralizator of allochthonous biologically recalcitrant but photoreactive CDOM and the linkage of this matter into lacustrine food web (microbial link). The pelagial food web consists of bacteria (bact), flagellates (flag), ciliates (cil) and (macro)zooplankton (zpl). The productivity of food web bases both on allochthonous and autochthonous organic matter, the latter contributing little to the concentration of CDOM in the lake. Generated from the idea of Molot LA and Dillon PJ (1997) Photolytic regulation of dissolved organic carbon in northern lakes. Global Biogeochemical Cycles 11: 357365. 48 Properties of Water _ Light, Photolytic Reactivity and Chemical Products Moran MA and Zepp RG (1997) Role of photoreactions in the formation of biologically labile compounds from dissolved organic matter. Limnology and Oceanography 42: 13071316. Tranvik LJ and Bertilsson S (2001) Contrasting effects of solar UV radiation on dissolved organic sources for bacterial growth. Ecology Letters 4: 458463. Vahatalo AV and Jarvinen M (2007) Photochemically produced bioavailable nitrogen from biologically recalcitrant dissolved organic matter stimulates the production of nitrogen-limited microbial food web in the Baltic Sea. Limnology and Oceanog- raphy 52: 132143. Zafiriou OC, Joussot-Dubien J, Zepp RG, and Zika RG (1984) Photochemistry of natural waters. Environmental Science and Technology 18: A358A371. Zepp RG (2003) Solar ultraviolet radiation and aquatic carbon, nitrogen, sulfur and metals cycles. In: Helbling EW and Zagarese H (eds.) UV Effects in Aquatic Organisms and Ecosys- tems, pp. 137183. Cambridge: Royal Society of Chemistry. Properties of Water _ Light, Photolytic Reactivity and Chemical Products 49 This page intentionally left blank HYDROLOGY Contents Hydrological Cycle and Water Budgets Atmospheric Water and Precipitation Snow and Ice Evapotranspiration Vadose Water Ground Water Ground Water and Surface Water Interaction Groundwater Chemistry Fluvial Export Fluvial Transport of Suspended Solids Streams Rivers Springs Wetland Hydrology Hydrological Cycle and Water Budgets T N Narasimhan, University of California at Berkeley, CA, USA 2009 Elsevier Inc. All rights reserved. Introduction The Earths geology, its atmosphere, and the phenom- enon of life have been profoundly influenced by water through geological time. One manifestation of this influence is the hydrological cycle, a continuous exchange of water among the lithosphere, the atmo- sphere, and the biosphere. The present-day hydrolog- ical cycle is characterized by a vigorous circulation of an almost insignificant fraction, about 0.01%, of the total water existing on the Earth. Almost all beings on land require fresh water for sustenance. Yet, remark- ably, they have evolved and proliferated depending on the repeated reuse of such a small fraction of available water. The partitioning of water among the compo- nents of the hydrological cycle at a given location constitutes water balance. Water-balance evaluations are of philosophical interest in comprehending the geological and biological evolution of the Earth and of practical value in environmental and natural- resource management on various scales. The purpose here is to outline the essential elements of the hydro- logical cycle and water budgets relevant to inland waters and aquatic ecosystems. Hydrological Cycle The hydrological cycle is schematically shown in Figure 1. Atmospheric water vapor condenses and precipitates as rain or snow. A small portion of this is intercepted by vegetation canopies, with the rest reaching the ground. A portion of this water flows over land as surface water toward the ocean or inland depressions, to be intercepted along the way by ponds, lakes, and wetlands. Another portion infil- trates to recharge the soil zone between the land surface and the water table, and the groundwater reservoir below the latter. Pulled by gravity, ground water can move down to great depths. However, because of the presence of low permeability earth layers, the downward movement is resisted, and water is deflected up toward the land surface to be discharged in streams, lakes, ponds, and wetlands. Water escaping the influence of resistive layers and moving to greater depths encounters geothermal heat. Geothermal heating too has the effect of countering downward movement and impelling ground water toward the land surface. At the land surface, surface water and discharging ground water are subject to evaporation by solar radiation and to transpiration by plants as they consume water for photosynthesis. Collectively referred to as evapotranspiration, this transfer of water back to the atmosphere completes the hydrological cycle. The components of the hydrological cycle, namely, atmosphere, surface water, and ground water (includ- ing soil water), are intimately interlinked over a variety of spatial scales (meters to thousands of kilometers) 51 and temporal scales (days to millions of years). Infor- mation on the volume of water stored in each compo- nent of the hydrological cycle, and the relevant spatial and temporal scales are summarized in Table 1. Water is a slightly compressible liquid, with high specific heat capacity and latent heats of melting and evaporation. It exists in solid, liquid, and gaseous phases within the range of temperatures over which life, as we know it, can sustain. Its bipolar nature enables it to form cage-like structures that can trap nonelectrolyte molecules as well as charged ions. For these reasons, water is an active chemical agent, effi- cient transporter of mechanical energy and heat, and a carrier of dissolved and suspended substances. Snow accumulation Snowmelt runoff Interception Infiltration Overland flow Evaporation Lake Storage Transpiration Streamflow Geothermal heat Ocean Percolation from snowmelt Percolation Water table Groundwater discharge to lakes, streams, and ocean Evaporation Precipitation Deep groundwater circulation Figure 1 Schematic description of the hydrological cycle: adapted from T. Dunne and L. B. Leopold, 1978, Water in Environmental Planning, p. 5. Table 1 Hydrological cycle: spatial and temporal scales Storage, % of Totala,b Spatial scalec Residence Timed Atmosphere 0.001 Km to thousands of km Days Surface watere 0.01 Meters to hundreds of km Weeks to years Soil water 0.05 Meters to tens of meters Weeks to years Ground water 2.1 Tens of meters to hundreds of km Days to millions of years Oceans and seas 95.7 Km to thousands of km Thousands of years Ice caps and glaciers 2.1 Km to thousands of km Tens of thousands of years a Total volume of water on Earth, 1.43 109 km3 . b From Unesco, 1971, Scientific framework for World water balance, p. 17. c Distance over which cycle is completed. d From Unesco, 1971, Scientific framework for World water balance, p. 17. e Includes lakes and reservoirs, river and stream channels, swamps. 52 Hydrology _ Hydrological Cycle and Water Budgets These attributes render water to be an extraordinary geological and biological agent that has endowed the Earth with features no other celestial object is known to possess. The hydrological cycle is driven mostly by solar energy and to a minor extent by geothermal heat. The Earths erosional and geochemical cycles exist due to waters ability to do mechanical work asso- ciated with erosion, chemically interact with rocks and minerals, and transport dissolved and suspended materials. Collectively, the hydrological, erosional, and geochemical cycles constitute the vital cycles that sustain life. The interrelationships among these vital cycles can be conveniently understood by examining the lithospheric components of the hydrological cycle. Hydrological Cycle: Lithospheric Components Surface water On the Earths surface, water breaks down rocks physically and chemically through weathering, aided by solar energy and by actions of microbes, plants, and animals. The products of weathering are transported as sediments (bedloads and suspended loads) and dissolved chemicals. In addition, water also transports leaf litter and other decaying vegetation and animal matter. The sedi- ments and organic matter together contribute to the cycling of life-sustaining nutrients. The habitats of flora and fauna along the course of a river depend, in very complex ways, on the texture of sediments as well as on their chemical makeup. A glimpse into the intricate influence of physical nature of sediments and the aquatic chemical environment on an organisms life cycle is provided by salmon, an anadromous fish. In the wild, salmon is hatched in gravelly stream beds that provide protection from predators and abundant supplies of oxygen to the eggs. Once hatched, the young fingerlings must have narrowly constrained aquatic chemical and thermal environment to survive as they migrate from a freshwater environment to a marine environment where they will spend their adult life. Soil water The soil zone lies between land surface and the water table, where water and air coexist. Soil water, which is held in the pores by capillary forces, is not amenable for easy extraction by humans. How- ever, plants have the ability to overcome capillary forces and extract water for their sustenance. Micro- bial populations constitute an integral part of the soil biological environment. With abundant availability of oxygen and carbon dioxide in the air, the soil is an active chemical reactor, with microbially mediated aqueous reactions. In the soil zone, water movement is dominantly vertical, and a seasonally fluctuating horizontal plane separates vertically upward evaporative move- ment from downward directed gravity flow. Water moving down by gravity reaches the water table to recharge the groundwater reservoir. The journey of water from the time it enters the groundwater reser- voir to the time it emerges back at the land surface may be referred to as regional groundwater motion. Regional groundwater motion constitutes a conve- nient framework for an integrated understanding of the formation of sedimentary rocks and minerals, and the areal distribution of soils and aquatic ecosystems on land. Ground water Infiltrating water enters the ground- water reservoir at high elevations, and driven by gravity, moves vertically down in areas of ground- water recharge. Depending on topographic relief and the distribution of permeable and impermeable layers, the vertically downward movement is resisted sooner or later, and the movement becomes subhor- izontal. With further movement, flow is deflected up toward the land surface in areas of groundwater discharge. Groundwater discharge typically occurs in perennial stream channels, wetlands, low-lying areas, and springs. In these discharge areas, surface water and ground water directly interact with each other, with important geological and biological conse- quences. For example, the spectacular tufa towers of Mono Lake in California represent precipitates of calcium carbonate resulting from a mixing of sub- aqueous thermal springs with the lake water. Hypor- heic zones, which play an important role in stream ecology, are groundwater discharge areas where stream flow is augmented by groundwater discharge. Regional groundwater flow provides a framework to interpret patterns of chemical processes in the subsurface. Water in recharge areas is rich in oxygen and carbon dioxide and has a significant ability to chemically break down minerals through corrosive oxidation reactions. However, available oxygen is consumed as water chemically interacts with the minerals along the flow path, and the oxidation potential of ground water progressively decreases along the flow path. In swamps and wetlands of discharge areas, water exists under strong reducing (anaerobic) conditions. Between these two extremes, ambient conditions of acidity (pH) and redox state (Eh) govern the chemical makeup of water as well as the types of minerals and microbial populations that are compatible with ambient water chemistry. In gen- eral, the cation content of ground water reflects the chemical make up of the rocks encountered along Hydrology _ Hydrological Cycle and Water Budgets 53 the flow path, and the anion content is indicative of the progress of chemical reactions. The concept of hydrochemical facies denotes the diagnostic chemical aspect of aqueous solutions reflect- ing the progress of chemical processes within the frame- work of regional groundwater motion. Given the concept of regional groundwater motion, and that of hydrogeochemical facies, one can readily see how the spatial distribution of various types of soils, and the distribution of different types of ecosystems over a watershed, must represent the profound influence of the lithospheric segment on the hydrological cycle. Regional groundwater flow pattern in the Atlantic Coastal Plain as deciphered from hydrochemical infor- mation is shown in Figure 2. Nutrient Cycling and Energy Balance A discussion of the hydrological cycle is incomplete without examining its connections to nutrient cycling and solar energy balance. A glimpse into connections to nutrient cycling can be gained by examining the role of water in the cycling of carbon, sulfur, and phosphorus. Almost all biological carbon originates in atmospheric car- bon dioxide through photosynthesis by plants and phytoplankton. Water, essential for the photosynthe- sis process, is transferred as water by plants from the soil via leaves to the atmosphere, completing the hydrological cycle. In the lithosphere, water plays a dominant role in the decomposition and mineraliza- tion of organic carbon on diverse time scales, ulti- mately producing carbon dioxide or methane to be returned to the atmosphere. Sulfur is a multivalent, redox-controlled chemical species which plays an important role in metabolic reactions of plants. Under reducing conditions, sulfur is insoluble in water. Sulfate, its most oxidized form, is water solu- ble, and it is in this form that sulfur usually enters plant roots. Sulfide minerals constitute the principal source of sulfur in the lithosphere, and they are oxi- dized in the presence of bacteria to sulfate and become available for uptake by plants. In plants, sulfur is fixed in a reduced form. Thus, sulfur of dead organic matter is mobilized by oxidizing waters to sulfate to sustain the sulfur cycle. Phosphorus, which plays several important roles in the biological processes of plants and animals, is water soluble only under very narrow ranges of redox and pH. It does not readily form gaseous compounds. Therefore, phosphorus cycling is almost entirely restricted to the lithosphere. Phosphorus cycling effectively main- tains biological habitats despite the severe aqueous constraints that limit its mobility. The hydrological cycle is driven largely by solar energy. Just like water, solar energy is also subject to cyclic behavior. On the land surface, the energy received as incoming solar radiation (insolation) is balanced partly by outgoing longwave radiation, partly as sensible heat by convecting air columns and partly as latent heat transferred by water from 500 sea level 500 1000 1500 PotomacR. PoluxentR. S e d i m e n t s BrandywineMd. ChesapeakeBeachMd. C r e t a c e o u s s e d i m e n t s T e r t i a r y Figure 2 Groundwater flow patterns inferred from hydrochemical facies in the Atlantic coastal plain (W. Back, 1960, Origin of Hydrochemical Facies of Groundwater in the Atlantic Coastal Plains). 54 Hydrology _ Hydrological Cycle and Water Budgets the land to the atmosphere. Of the total solar radia- tion received from the sun on land, the amount of energy returned by water to the atmosphere amounts to about 46%, a major fraction. Any significant per- turbation of this contribution will have influence global climate. Summary The concept of hydrological cycle is elegantly simple. But, its importance in the functioning of the geologi- cal and biological Earth is profound, transcending water itself. It plays an overarching role in the cycling of solar energy, sediments, and chemical elements vital for the sustenance of life. Although it is clear that contemporary ecosystems reflect an evolutionary adaptation to the delicate linkages that exist among the various components of the hydrological cycle, it is also apparent that evolving life must have influenced the evolution of the hydrological cycle over geological time. Life, it appears, is simultaneously a product of the hydrological cycle and its cause. Water Budgets Framework Despite advances in science and technology, climate remains outside human control and manipulation. Humans, just as plants and animals, have to pattern their existence submitting to the variability of cli- mate. However, surface water, soil water, and ground water lie within reach of human control, to be man- aged for human benefit. In this context, the concept of water budgets becomes relevant. Given a volume element of the Earth with well- defined boundaries, water budget consists in quanti- fying the relationships among inflow, outflow, and change in storage within the element. This simple concept is as valid over the Earth as a whole treated as a volume element, over a river basin, or over a small rural community. In a world of stressed water resources, water budget is assuming an ever increas- ing importance as a framework for wise and equitable water management. Water is always in a state of motion, and its budget is governed by the simple notion that inflow must equal change in storage plus outflow. Symbolically, this may be stated as P E RSu RGw DSu DSo DGw DH 1 where P is precipitation, E is evapotranspiration, R is runoff, Su is surface water, Gw is ground water, So is soil water, DH is diversion by humans, and D denotes change in storage. If the time interval of interest is smaller than a season, the terms involving change in storage cannot be neglected, the system being under transient conditions. If, however, the time interval of interest is a year or several years, seasonal increases and decreases in storage will effectively cancel out, and the water budget equation reduces to a steady- state balancing of inflow and outflow P E RSu RGw DH 2 Implicit here is the assumption that precipitation constitutes the only inflow into the volume element, which is reasonable if one considers a watershed enclosed by a water divide, without any water import. Clearly, if the volume element of interest is defined by open boundaries, terms representing water import and export have to be added to the equations. Assessment of Components The simplicity of the above equations belies the diffi- culties inherent in assessing the different components involved. Perhaps the most widely measured quanti- ties in water budgets are precipitation and surface runoff. Rainfall data from aerially distributed rain- gauging stations are integrated over space to arrive at the total volume of water falling over an area during a period of interest. Runoff estimated at a given loca- tion on a stream with flow meters or river-stage data supplemented by rating curves, represents outflow from the watershed upstream of that location. Evapotranspiration Experience has shown that eva- potranspiration constitutes a significant percentage of precipitation over the land surface. Yet, quantification of evapotranspiration is a difficult task. The gravimet- ric lysimeter provides a way of experimentally estimat- ing evapotranspiration from a soil mass of the order of a few cubic meters in size. Although of much value as tools of research, lysimeters are helpful in estimating evapotranspiration only over small areas. For water- sheds and river basins, it is customary to use a combi- nation of empirical and theoretical methods. In one such approach, the concept of potential evaporation plays a central role. Potential evaporation is under- stood to be the height of column of water that would be evaporated from a pan at a given location, assuming unlimited supply of water, as from a deep lake. If precipitation at the location exceeds potential evapora- tion, the soil is assumed to hold a maximum amount of water in excess of gravity drainage. If precipitation is less than potential evaporation, then the actual evapo- transpiration will be limited to what precipitation can supply. In this case, empirical curves are used to Hydrology _ Hydrological Cycle and Water Budgets 55 estimate soil moisture storage based on precipitation deficit and the maximum water-holding capacity of the soil. With the availability of instruments of increased sophistication and super computers, energy methods are increasingly sought after to estimate evapotranspi- ration from watershed scale to continental scale. In these methods, the goal is to carry out a solar energy budget and isolate the amount of energy that is trans- ferred by water from the land surface to the atmo- sphere as latent heat. This estimate is then converted to evapotranspiration. To support this model, data are generated from detailed micrometeorological measure- ments such as short-wave and long-wave radiation, temperature, humidity, cloud cover, and wind velocity. Another method for estimating evapotranspiration is to carry out an atmospheric water balance in a verti- cal column overlying the area of interest. In this method, evapotranspiration is set equal to the sum of precipitation and change in water vapor content of the column, less the net flux of water laterally entering the column. Soil-water storage In the field, water content of soils can be profiled as a function of depth with the help of neutron logs or by Time Domain Reflectometry. In principle, one can empirically estimate change in soil- water storage by carrying out repeat measurements with these instruments. However, these methods are of limited value when estimates are to be made over large areas. The concept of field water capacity, used widely by soil scientists and agronomists, denotes the quantity of water remaining in a unit volume of an initially wet soil from which water has been allowed to drain by gravity over a day or two, or the rate of drainage has become negligible. The water that remains is held by the soil entirely by capillary forces. Field capacity depends on soil structure, texture, and organic content and is commonly measured to help in scheduling irrigation. Empirical curves presented by Thornthwaite and Mather (1957) provide correla- tions among field water capacity, water retained in soil, and the deficit of precipitation with reference to potential evaporation. These curves can be used to estimate change in soil-water storage. Groundwater storage Changes in groundwater stor- age occur due to two distinct physical processes. At the base of the soil zone, as the water table fluctuates, change in storage occurs through processes of satura- tion or desaturation of the pores. In this case, change in groundwater storage per unit plan area is equal to the product of the magnitude of the water-level fluc- tuation and the specific yield of the formation, a parameter that is approximately equal to porosity. In the case of formations far below the water table, water is taken into storage through slight changes in the porosity, depending on the compressibility of the formations. In this case, change in groundwater storage can be estimated from the product of water- level fluctuation and the storage coefficient of the formations. Groundwater runoff The movement of water in the subsurface is quantified with Darcys Law, according to which the volume of water flowing through a given cross sectional area per unit time is equal to the product of the hydraulic conductivity of the forma- tion, the gradient of hydraulic head, and the cross- sectional area. In the field, hydraulic gradients can be obtained from water table maps. These, in conjunc- tion with the known hydraulic conductivity of the geological formations can be used to estimate groundwater runoff. Table 2 Statewide water balance, California m3 (mafa ) Water year (Percent of normal precipitation) 1998 (171%) 2000 (97%) 2001 (72%) Precipitation 4.07 1011 (329.6) 2.32 1011 (187.7) 1.72 1011 (139.2) Imports: Oregon/Nevada/Mexico 9.00 109 (7.3) 8.63 109 (7.0) 7.77 109 (6.3) Total inflow 4.16 1011 (336.9) 2.40 1011 (194.7) 1.79 1011 (145.5) Evapotranspirationb 2.58 1011 (208.8) 1.62 1011 (131) 1.53 (124.2) Exports: Oregon/Nevada/Mexico 1.85 109 (1.5) 1.11 109 (0.9) 8.63 108 (0.7) Runoff 1.49 1011 (120.8) 8.46 1010 (68.6) 4.30 1010 (34.9) Total outflow 4.08 1011 (331.1) 2.48 1011 (200.8) 1.97 1011 (159.8) Change in surface water storage 8.88 109 (7.2) 1.60 109 (1.3) 5.67 109 (4.6) Change in groundwater storage 1.72 109 (1.4) 5.55 109 (4.5) 1.20 1010 (9.7) Total change in storage 7.15 109 (5.8) 7.15 109 (5.8) 1.76 1010 (14.3) a Million acre feet. b Includes native plants and cultivated crops. 56 Hydrology _ Hydrological Cycle and Water Budgets Two Examples Global water balance Between 1965 and 1974, the International Hydrological Decade Program of UNESCO did much to focus attention on the impera- tive to judiciously manage the worlds freshwater resources. An important contribution to the efforts of IHD by the Russian National Committee was the pub- lication, World Water Balance and Water Resources of the Earth (Unesco, 1978), which provided detailed estimates of water balance for the different continents, and for the Earth as a whole. The general finding was that for the world as a whole, total annual precipitation is of the order of 113cm, or about 5.76 105 km3 . Globally, this precipitation is balanced by an equal magnitude of evapotranspiration. However, an im- balance exists between precipitation and evapotran- spiration, if land and the oceans are considered separately. Over land, average annual precipitation is about 80 cm, or 1.19 105 km3 . Of this, evapotrans- piration constitutes 48.5 cm (60.6%) and runoff constitutes 31.5 cm (39.4%), indicating a deficit of precipitation in comparison to evapotranspiration. Over the oceans, the average annual precipitation is about 127 cm, or 4.57 105 km3 , while evaporation is about 140 cm. The excess of evaporation over precipitation over the oceans is equal to the runoff from the land to the oceans. California With a land area of 409 500 km2 , and spanning 10 of latitude and longitude, California exhibits remarkable diversity of physiography, cli- mate, flora, and fauna. The Department of Water Resources of the State of California periodically pre- pares water balance summaries to aid state-wide water planning. The DWRs latest water balance esti- mates are instructive in that they provide comparison of water budget for an average year with those of a surplus year and a deficit year (California Department of Water Resources, 2005). Salient features are sum- marized in Table 2. It is interesting to note from the table that (1) ground water is being over pumped even during surplus years, (2) California experiences a def- icit of about 3% even during an average year, and (3) evapotranspiration varies from 62% during a sur- plus year to as much as 85% during a drought year. Epilogue Modern science has shown that the observed behav- ior of the hydrological cycle can be understood and explained in terms of the laws of mechanics and thermodynamics. However, the ability of modern sci- ence to describe the hydrological cycle in precise detail and to predict the future behavior of components of the hydrological cycle with confidence is severely lim- ited. The limitation arises from the many spatial and temporal scales in which the components interact, the complexity of processes, difficulties of access to obser- vation, and sparsity of data, not to mention the role of living beings that defy quantification. Yet, we have to draw upon our best science so as to use the worlds limited supplies of fresh water wisely and equitably. This goal will be best achieved if we recognize the limitations of science, moderate our social and eco- nomic aspirations, and use science to help us adapt to the constraints imposed by the hydrological cycle. Throughout history, humans have been fascina- ted with water. Although modern science has been successful in elucidating the details of the functioning of the hydrological cycle, its essential features were astutely recognized and viewed with awe centuries (perhaps even millenniums) before Christ in China, India, Greece, and Egypt. It is therefore fitting to conclude this discussion of the hydrological cycle with a psalm from the Hindu scripture: The waters which are from heaven, and which flow after being dug, and even those that spring by themselves, the bright pure waters which lead to the sea, may those divine waters protect me here (Rig-veda, VII 49.2). See also: Atmospheric Water and Precipitation; Chemical Properties of Water; Evapotranspiration; Ground Water and Surface Water Interaction; Ground Water; Groundwater Chemistry; Phosphorus; Physical Properties of Water; Redox Potential; Streams; Vadose Water. Further Reading Encyclopedia Britannica (1977) Hydrological Cycle 9: 102116. Back W (1960) Origin of hydrochemical facies of groundwater in the Atlantic Coastal Plains, Report, 21st Session, Int. Geol. Congress, Copenhagen, Pt. 1, pp. 8795. Freeze RA and Cherry JA (1979) Groundwater. Englewood Cliffs, New Jersey: Prentice Hall, 604 pp. Narasimhan TN (2005) Pedology: A hydrogeological perspective. Vadose Zone J. 4: 891898. Thornthwaite CW and Mather JR (1957) Instructions and tables for potential evapotranspiration and water balance. Publica- tion in Climatology, Vol. 10, No. 3. Centerton, New Jersey: Thornthwaite and Associates. U.S. Geological Survey (2007) The Water Cycle, Complete Summary, Hydrology _ Hydrological Cycle and Water Budgets 57 Atmospheric Water and Precipitation K Fienberg and E Foufoula-Georgiou, University of Minnesota, Minneapolis, MN, USA 2009 Elsevier Inc. All rights reserved. Introduction Atmospheric water and precipitation play a key role in the global water cycle, comprise a conduit between oceanic and inland waters, and provide the main forcing variable for surface hydrologic processes. The dynamics of water in the atmosphere can be categorized into three general processes within the hydrologic cycle: evaporation from the surface as water enters the atmosphere; transport of water by atmospheric processes; and precipitation as water returns to the surface. Of these, it is precipitation that is the direct driving force for inland water pro- cesses such as runoff, soil and groundwater storage, and then stream flow. Hence, from the view-point of surface hydrology, the final result of atmospheric water movements, and precipitation, is the quantity of greatest interest. Precipitation forms the input of many hydrological models, and as such, measurements and model pre- dictions of precipitation are vital in understan- ding inland waters. Precipitation has been measured for centuries, and has been the subject of scien- tific investigation at least since Pierre Perrault and Edme Marriotte related measured rainfall to the flow of the Seine in the seventeenth century. However, despite advances in both direct and remote measure- ment technologies, and the development of more powerful and sophisticated computer models, both measurement and modeling of precipitation remain a challenge. One of the major reasons for this is the high degree of variability in both time and space. Although water vapor has been estimated to have an average life cycle in the atmosphere on the order of 10 days, observations show variability and structure in precipitation patterns from time-scales as short as seconds to as long as multiyear cycles in some regions. As a general guideline, short-lived temporal patterns are generally associated with features of smaller spa- tial extend, while longer-term patterns are associated with processes that take place at larger spatial scales. It is clear that there are a large number of different processes causing this variability: from turbulent transport of raindrops at short time scales, to synop- tic events with lifecycles measured in hours or days, to multiyear climatic patterns such as the El Nino- Southern Oscillation. Nevertheless, this range of different processes combines to create highly inhomo- geneous precipitation fields with fluctuations at almost all wavelengths. This complex structure in space and time has long raised questions for the mea- surement of precipitation, i.e., if a rain gauge has an aperture measured in centimeters, how can hourly rainfall readings be extrapolated to regions surround- ing the gauge? What about daily gauge totals? If one has satellite-based estimates of rainfall every few hours over a large area, what can one say about the precipitation intensities between observation times? How can observations with different instruments, which have different resolutions, be compared? Simi- larly, the variability over a wide range of scales also poses problems for the numerical modeling of rain- fall, not only in the issue of comparison and initiali- zation with measurements at different scales, but also on the fundamental questions of what processes, and at which scales, need to be included in the model, and how to accurately create closure schemes to account for those processes occurring at scales below the resolution of the model. As will be presented in the subsequent sections of this work, many of these questions have already been addressed using careful analysis of precipitation measurements and models that specify how the statistics of precipitation depend on scale. Other scale-related problems for measure- ments and models remain unresolved. The question of the nature of rainfall variability at different scales is not only important for understand- ing precipitation itself, but also for modeling its effects on surface hydrology. Processes that are driven by precipitation, such as soil water-storage and run- off, are generally nonlinear and thought to depend on threshold levels of precipitation. Therefore, as studies have shown, modeling these processes requires know- ledge of the spacetime distribution of the precipita- tion field and not simply the mean values. Thus, the results of modeling these processes are dependent on both the resolution of the precipitation input and the scale (or resolution) of the model itself. In light of the importance of the spatial and tempo- ral patterns in precipitation, and their dependence on scale, this work surveys the scientific investiga- tions of precipitation with a particular focus on spatialtemporal structure. First, in the following sec- tion, we briefly outline the various processes involved in precipitation formation to examine the origins of this structure. Subsequently, the techniques of pre- cipitation measurement, each of which can be used to measure a different range of precipitation vari- ability, are reviewed. Precipitation modeling is then 58 described, with emphasis on scale-invariant statistical models that can describe the multiscale variability of precipitation in a relatively parsimonious manner. Precipitation Formation Water Vapor in the Atmosphere Water enters the atmosphere via the process of evap- oration from both the land-surface and the ocean. This includes the process of transpiration, which is the evaporation of water vapor into the atmosphere through the vascular system of plants. Evaporation from the land surface contributes, on a global aver- age, approximately two-thirds of the total moisture available for precipitation over land. However, the evaporation rate at any particular time and place will depend on the amount of surface water present, the available energy to allow change of phase from liquid to vapor, and the atmospheric conditions to remove the evaporated molecules from the surface where they may condense again. Thus, the evapora- tion rate will change with location and time, creating differences in the level of water vapor in the atmos- phere, and thus providing one cause of variability in precipitation. Over land, there are daily and sea- sonal cycles in evaporation due to the cycles of solar radiation input and temperature, and hence the avail- able energy for evaporation. Variations in space are caused by changing surface water, land cover, and vegetation with location. Over the ocean, where sur- face temperatures are not as closely linked to the solar radiation cycles due to energy storage by the deep water, researchers have identified other cycles in sea- surface temperature that affect evaporation rates. One example is the multiyear El Nino phenomenon (part of the Southern Oscillation), in which changes in currents in the Pacific Ocean every 28 years move warm water from the west Pacific and the Indian Ocean to the east Pacific. Higher water temperature causes extra evaporation and drives rain processes, causing higher rainfall over the west coast of the Americas. Simultaneously, lower sea surface tempera- tures cause drier conditions in southeast Asia and northern Australia. Once water vapor has entered the atmosphere via evaporation, it is transported by the atmosphere until it is released as precipitation. The concentration of water vapor decreases rapidly with height, with 50% of the total column water vapor being found in the first 1 or 2 km of the atmosphere. In the generally turbulent lower atmosphere, at least at scales above the homogeneity scale (on the order of millimeters), transport by molecular diffusion is inconsequential in comparison to advection by the wind velocity field. The turbulent velocity field v is described by the NavierStokes equations for incompressible fluids: @n @t n rn 1 r rp mr2 n f @ @t rnr 0 1 where r is the fluid density, m is the viscosity, and f is the forcing term. This system has been studied for decades, with notable early contributions by Reynolds, Richardson, Kolmogorov, and Obhukhov, and for high Reynolds number, water vapor flux has been shown to be highly intermittent, nonstationary with stationary increments, have fat-tailed distribu- tions, and show scale-invariant patterns. If the water vapor is assumed to be a passive scalar, the specific mass flux of water vapor is then given by F rvv, where rv is the water vapor density. Thus, the water vapor flux should also be highly variable, nonsta- tionary, and intermittent. Indeed, numerical studies for passive scalar advection have shown that they can be even more intermittent than the underlying velocity field. In reality, of course, water vapor is not a passive scalar, since it affects the energy budget and thermo- dynamics of the atmosphere in a number of ways. For example, reduction (or increase) in water vapor through condensation (or evaporation) will release (or absorb) energy, thereby changing the temperature of the air particle, and making the pressure and forc- ing terms in eqn [1] functions of water vapor density. This process of energy release with condensation affects the stability of the atmosphere. The saturation vapor pressure of water is an increasing function of temperature (with the GoffGratch formula being the standard model to give exact values) and hence cooling can cause condensation if the vapor pressure is at saturation. This can affect atmospheric stability, since if the cooling associated with the rise of a parcel of air causes condensation and releases energy (to partially offset the cooling), the rate of change in temperature with height will be lower. Therefore the saturated or moist adiabatic lapse rate is lower than the dry adiabatic lapse rate of 9.8 K km1 . If the temperature decrease with elevation in the atmos- phere is larger than the adiabatic lapse rate, the atmos- phere is unstable, and rising air parcels will tend to continue rising. Rising air and condensation are important ingredients in cloud formation, and so the distribution of water vapor not only determines the amount and type of cloud formation through the sup- ply of water, but also through its effects on atmos- pheric stability. Hydrology _ Atmospheric Water and Precipitation 59 Cloud Formation Since saturation vapor pressure is mainly a function of temperature, and water vapor will condense into water or ice particles if the vapor pressure is at or above saturation (supersaturation), there are essen- tially two ways to cause cloud droplet formation: introduce additional water vapor, or cool the air already containing some water vapor to reduce the saturation vapor pressure. Cooling is the most com- mon cause of cloud formation, as the addition of water vapor only occurs through evaporation and usually happens close to the surface. This cooling can be achieved through radiative cooling, the air mass moving over a colder surface or the mixing of a warm moist air mass with a colder one, but in general these cooling mechanisms are inefficient and produce only light clouds or fogs. A more effective manner of cooling, and that which leads to the major- ity of precipitation, is through lifting, as the decrease in pressure with height leads to cooling through expansion, as can easily be shown through the adia- batic gas relations. This lift can be generated by air moving over mountains, by the air being heated from below, or by the collisions of air masses in a frontal system when warm moist air is forced upwards to move over colder denser air. The nature and scale of the uplift mechanism, along with the degree of water vapor present and the stability of the atmosphere, determine the type of cloud system formed. If the atmosphere is stable, or capped by an inversion, and the lifting mechanism is not overly strong but wide in extent, stratiform clouds may form: these clouds are vertically thin and horizontally wide. If the lifting mechanism is strong, such as from heating, and the atmosphere is unstable, which reinforces any lifting, convective cells may form that are of greater vertical extent, but may be smaller in the horizontal direc- tions or at least have a greater degree of horizontal structure. On average, convective type clouds tend to produce more intense, but more localized, precipi- tation than stratiform clouds. In practice, cloud sys- tems combine stratiform and convective features to different degrees and a thorough exploration of cloud types is beyond the scope of this article. Once the cooling due to lifting has caused the air in some region to become supersaturated, water or ice particles will condense, depending on the temper- ature and the cloud condensation nuclei (CCN) available in the air. CCN are aerosol particles sus- pended in the air on which water can condense, and can consist of dust, smoke, salt, and a range of other substances such as pollutants produced by industry. The number and type of CCN affect the cloud droplet distribution and hence the chance of precipitation: a higher concentration of CCN can lead to the formation of many droplets. Because there is a finite amount of supersaturated water, all else being equal, a large number of droplets means that the average drop-size is smaller, and hence there is less chance of droplets growing large enough to fall out of suspension as precipitation. Conversely lower CCN concentrations produce fewer but larger droplets, all else being equal. This can be observed in the difference in cloud droplet concentration between marine cumulus clouds, which have fewer CCN (on the order of 102 cm3 ), and continental cumulus clouds, which have a higher CCN concen- trations (on the order of 103 cm3 ). The presence of aerosols also affects the distribution of ice particles, because small droplets of pure water will not freeze until below 39 C, but certain types of ice nuclei in the water can allow the freezing of ice particles with significantly higher temperatures: up to 15 C for some inorganic soil particles and up to 4 C for certain organic molecules from plants or plankton. Thus, the concentration and type of aerosol particles also influences the distribution and type of cloud particles and precipitation. From Cloud Particles to Precipitation Directly after forming, ice and liquid cloud particles have radii on the order of micrometers or less, making them easily small enough to remain suspended. Pre- cipitation depends on whether the cloud particles can grow large enough to fall out of the updrafts and not to evaporate away during their fall. The exact size required for this will vary based on the meteorologi- cal conditions, but a radius on the order of 100 mm is usually a minimum. The growth of liquid-water cloud droplets is dominated by condensation when they are small, but growth above about 10 mm is driven by collision and coalescence of drops as they are advected by the moving air and later as they begin to fall under their increasing weight. Ice particles can grow larger than water droplets by deposition directly from the vapor phase, since the saturation vapor pressure over ice is lower than that over liquid water. Indeed, because of this, ice particles in mixed phase clouds below freezing temperatures can grow by robbing water from the supercooled liquid-water droplets by the Bergeron process. Ice particles can also grow by collision with supercooled water drop- lets, as the water droplets snap-freeze onto them this is called riming, and is the process that produces graupel and in the extreme case, hail. Finally, ice particles can also grow to precipitable size through collision and aggregation with other ice particles. 60 Hydrology _ Atmospheric Water and Precipitation Thus, the selective growth of some cloud particles to precipitation involves a number of competing pro- cesses, especially in commonly occurring mixed-phase clouds, which introduces another process of variability at small scales. Finally, just like the water vapor, the cloud particles and precipitation are being advected (to a greater or lesser extent depending on their mass) by the nonlinear, intermittent, and multiscale turbulent fluid flow in the atmosphere. Precipitation Observations Although it is possible to trace in a qualitative fashion the timeline of processes that lead to precipitation formation, from evaporation, advection of water vapor, to cloud formation and cloud droplet growth, the fact that these processes are complex, inter- connected, nonlinear, and operating over a range of scales means that it is still an open problem of how to combine them into a model that reproduces the spacetime distribution of precipitation. But mea- surements of precipitation allow direct observation of the final results of these processes: precipitation on the ground. The three main methods currently used for measuring precipitation are rain gauges, ground-based remote sensing using radar, and space- based remote sensing with a range of instruments. Rain Gauges The traditional method for measuring precipitation is through gauges that catch and measure rain or snow directly. Types of gauges range from a simple storage container that does not record the precipita- tion level itself, to weight measuring gauges, tipping bucket gauges that count number of bucket tips, and the modern optical precipitation gauge that records the entrance of each drop into the gauge as it disturbs a laser beam. For rainfall measurements, the major source of error is the distortion of the wind field by gauges mounted above the ground. The gauge forms an obstacle to the wind-flow, increasing the wind flow over the gauge and creating eddies around it. Since the precipitation is moved by the wind, this reduces the total entering the gauge by an amount depending on the wind speed, rain intensity, and gauge geometry, with losses on the order of 10% of the rainfall total being possible. While correction schemes for this have been developed by Sevruk and others, the World Meteorological Organization recommends using pit-gauges, i.e., gauges mounted in pits below the ground surface and hence sheltered from the wind, as the reference to calibrate other gauge types. Other errors for rain include smaller losses to splashing and evaporation. Accurately measuring snow presents greater diffi- culties than measuring rainfall, even though standard gauges can be modified for snow by adding antifreeze to weighing gauges and heating tipping-bucket gauges to melt the snow. One reason for the difficulty is that the terminal fall velocity for snow flakes is much lower than that for water droplets, and they are much more easily transported by the wind, mean- ing that the error due to wind distortions around the gauge can be as high as 50% in worst-case conditions. As a result of these and other difficulties, it is recom- mended that a specially designed gauge for snow, such as the universal gauge of Cox, be used, prefer- ably in combination with wind-shielding. Despite the various sources of error, gauges are the only direct measurements of precipitation, and remain the most accurate source of precipitation information at any point in space and time. In particular, gauges can give very accurate descriptions of the structure and distribution of precipitation in time. Figure 1(a) shows an example of high-resolution rain-gauge data from the Iowa Institute of Hydraulic Research, University of Iowa, which shows variability across a range of tem- poral scales. In particular, the power spectrum of the data shown in Figure 1(b) shows variability decreasing with decreasing scale (increasing frequency) in an approximately power law relationship (a straight line on the loglog graph) between scales of around 1 min and 1 h. The limitation of gauge measurement is that gauges are usually sparsely spread over an area, and gauge apertures are on the order of centimeters, whereas hydrologic processes depend on the entire precipita- tion field over a catchment area that may have an area on the order of hundreds of kilometers. This is a long studied problem in hydrology, and a range of methods have been developed over the years to convert point gauge measurements to area values, beginning with Thiessens polygon area-averaging method, and going through surface fitting methods using interpolation or smoothing, to objective analysis and kriging. All of these methods depend on assumptions about the smoothness or statistical distribution of the precipita- tion field, which has been shown in more recent times to be more intermittent than most of these methods postulate. For more information on the spatial variability of the precipitation field, measure- ments from instruments other than rain gauges are required. Radar Quantifying the spatial variability of precipitation fields requires estimating the precipitation rate over a large area and a relatively short sampling interval: Hydrology _ Atmospheric Water and Precipitation 61 one of the most useful instruments to do this is land-based Doppler radars. Since rain and ice par- ticles reflect electromagnetic radiation that has a wavelength on the order of centimeters (by the Ray- leigh scattering process), radars emitting pulses at these wavelengths can estimate the amount of precipi- tation by measuring the reflected radiation. The frac- tion of radiated power that is reflected, or the reflectivity Z, has been found to relate to the precipita- tion rate R via the so-called ZR relation, specifically: Z aR b 2 where a and b are constants that vary with the calibra- tion of the radar, ground clutter, beam-broadening, and most importantly, the type of precipitation (rain or snow, convective or stratiform, continental or marine, etc.). The uncertainty due to precipitation-type can be reduced using dual-polarization radar, which adds an extra source of information because different precipi- tation types have different effects on the polarization of the reflected radiation. In this way, a Doppler radar can provide estimates of precipitation over an area of hundreds of kilometers, with a spatial resolution on the order of 15 km, every few minutes. An example of radar-retrieved precipitation rate is found in Figure 2. We can examine how the variability of rainfall depends on spatial scale by observing the power spectrum from radar data in Figure 3, which shows variability over a wide range of scales, and a power law over all observed scales. A large fraction of the United States is covered by the NEXRAD system of 130 WSR-88D radar stations, which are S-band (or 10 cm wavelength) Doppler radars that have a range of 230 km, an average resolution of 2 km (actual resolution is a function of the distance from the radar), and record precipitation intensities every 6 min. Although initi- ally they were set-up without polarization, the National Oceanic and Atmospheric Administration (NOAA) has a program underway to convert these stations to dual-polarization radars by 2010. Other developed countries have similar terrestrial radar net- works, such as the Central European Weather Radar Network (CERAD), or are working on them. These radar networks provide high spatial and temporal resolution precipitation data that can be used as an input for hydrologic models, but there are still vast areas of the globe, especially in poorer or developing countries, that are not covered by terrestrial radar. There are also limits to the coverage of ground-based radar in some mountainous areas where the field of view is interrupted by the terrain. To investigate the distribution of precipitation in these areas, one must look to satellite observations. Satellite Remote Sensing There are a number of satellite-mounted instruments that are used to estimate precipitation levels, but they can be divided into two main groups. The first are those instruments that attempt to retrieve precipita- tion intensities through the active or passive measure- ment of microwave radiation. Remote sensing in the microwave frequencies is particularly applicable to 0 (a) (b) 0 10 20 Rainrate(mm/hr) 100 1000 100 10 Wavelength (min) 1 0.1 105 1010 Powerspectraldensity 30 40 100 200 300 Time (min) 400 500 600 Figure 1 Rain gauge data from a high resolution optical gauge, with part (a) showing the data series in time, and part (b) showing the power spectrum of the data. 62 Hydrology _ Atmospheric Water and Precipitation precipitation retrieval because microwave propaga- tion is sensitive to the presence of large water and ice particles, but less affected by smaller cloud parti- cles (unlikely to precipitate) and other atmospheric attenuation. Passive microwave sensors attempt to determine precipitation rates based on the increased natural emission of radiation, and hence higher observed brightness temperatures, due to the presence of precipitation. Alternatively, active sensors measure the scattering of an emitted beam. In this sense, they use the same general concept as earth-based radars, but with the added difficulties of the increased dis- tance, the large column of atmosphere to penetrate to retrieve precipitation at the ground, and more background noise. Both active and passive microwave data must be corrected for these effects. Therefore, the uncertainties in the precipitation measurements are significantly higher than for earth-based radar. The advantage of the space-based measurements is their extremely large range of spatial coverage. Commonly used examples of microwave instruments used to measure precipitation from space are: the Special Sensor Microwave/Imager (SSM/I) that is part of NASAs Pathfinder Program; the Precipitation Radar (PR) and TRMM Microwave Imager (TMI) that are included in NASAs Tropical Rainfall Mea- suring Mission (TRMM); the Advanced Microwave Scanning Radiometer (AMSR-E) aboard the Aqua spacecraft; and the Cloud Profiling Radar (CPR) aboard the CloudSat satellite. An example of data collected by the TMI instrument on TRMM can be seen in Figure 4, which shows the weekly accumu- lated precipitation over the entire globe at 0.25 resolution. Note the high degree of structure on very large scales that can be captured with satellite imaging, compared to the relatively local-scale detail observed by ground-based radar image (cf. Figure 2). The second type of precipitation estimations made via satellite remote sensing uses passive imaging radiometers in the infrared, near-infrared, or visible parts of the spectrum. These wavelengths are more sensitive to cloud properties other than precipitation, such as cloud-top temperature, total cloud liquid water path, mean droplet radius, and cloud spatial 50 450 400 350 300 250 Distance(km) 200 150 100 50 Precipitation rate (mm/hr) 60 50 40 30 20 10 100 150 200 250 Distance (km) 300 350 400 450 Figure 2 Precipitation rate from a single scan with a Doppler weather radar from the NEXRAD station KPBZ at Pittsburgh, PA, USA (coordinates 40.5317 N, 80.2181 W). 100 103 102 101 Wavenumber (km1 ) Powerspectraldensity 100 105 1010 Figure 3 The power spectrum of precipitation field observed by a single scan with a ground-based radar from the NEXRAD station KPBZ at Pittsburgh, PA, USA (coordinates 40.5317 N, 80.2181 W). Hydrology _ Atmospheric Water and Precipitation 63 extent. The precipitation retrieval therefore relies on relationships between these other cloud properties and precipitation intensity, either through empirically derived look-up tables (or database inversion) or simplified precipitation models. Since they are less direct estimates, the precipitation readings from this method are considered more uncertain than the satel- lite microwave or radar measurements. However, these less direct estimates have the advantage of not requiring a specialized instrument, but instead using measurements from radiometers that are found on many operational satellites such as NOAAs Geosta- tionary Operational Environmental Satellite (GOES) series or Japans Geostationary Meteorological Satel- lites (GMS). This allows for a greater frequency of observations in time than is possible using the specialized microwave instruments currently moun- ted on only a relatively small number of satellites: specifically the visible and infrared satellite products are usually produced hourly, as opposed to a 3-h or longer gap between microwave precipitation images. NASAs TRMM mission now produces an hourly hybrid product that uses indirect infrared estimates that are calibrated every 3 h with the more accurate microwave data. Satellite measurements of precipitation have the advantage of extremely wide spatial coverage over the globe, but are less accurate and have lower spatial and temporal resolutions than do ground-based weather radars. In particular, while spatial resolution seems to be increasing significantly with each genera- tion of satellites, temporal resolution does not seem to be increasing at the same rate, as it depends not so much on the instrument but on the frequency of satellite overpass. This remains a challenge for the satellite remote sensing of precipitation. Modeling Precipitation Whether estimated by gauges, ground-based radars, or satellites, precipitation exhibits variability at all spacetime scales: from seconds to years, and from meters to hundreds of kilometers. Understanding this variability is not only important for hydrologic appli- cations, but even for the basic tasks of comparing, validating, and merging estimates of precipitation made at different scales by different sensors. Direct numerical models of clouds and rainfall are certainly possible, combining computational fluid mechanics of atmospheric flow with a model of the so-called microphysics of cloud and rain particles, and these cloud-resolving models (CRMs) form a strong area of ongoing research. They often involve nested model levels, with coarse resolution models to capture large- scale environmental forcings and provide boundary conditions for fine resolution models that include the cloud microphysics. This presents difficulties not only because of the high degree of computing power required, but because of challenges in developing accu- rate models or parameterizations of cloud microphys- ics. This is due to the fact that there are many complex processes involved in droplet formation, growth, and fall-out, and that direct observation of these in-cloud processes, for either validation or initialization pur- poses, is difficult. Despite these difficulties, research continues apace on improving CRMs and data- assimilation methods for quantitative precipitation forecasts. Also, at larger scales than it is currently feasible to run a fully detailed CRM, regional and global circulation models (GCMs) of the atmosphere include successively more coarse-grained parameteri- zations of cloud and precipitation processes. How to improve these parameterizations while maintaining reasonable model complexity and running-time is yet another challenge in precipitation modeling. Scale-Invariant Statistical Models For applications at scales below the ones well resol- ved by numerical models, and to even verify how well numerical models are in fact reproducing the spacetime patterns of precipitation, statistical models of precipitation are required. Early recognition of 4 10030 May 2007 2100 UTC 300 500 700 900 1100mm 8 12 16 20 24 28 32 36 40 44inches Figure 4 Total precipitation accumulated over a week from the microwave instruments on the TRMM satellite. 64 Hydrology _ Atmospheric Water and Precipitation the importance of small-scale variability of rainfall in space and time for hydrological applications led to stochastic point-process models or phenomenologi- cal spatiotemporal models of rainfall. However, these models tended to have a large number of parameters to fit, and to be scale-dependent in their application. From the late 1980s to early 1990s, the desire to unify the description of precipitation over scales, and reduce the number of model parameters, inspired the adop- tion of ideas and tools from turbulence modeling and fractal geometry. This led to the development of vari- ous scale-invariant models of precipitation. The basic meaning of (stochastic) scale invariance is that the variability of precipitation exhibits a statistically self- similar structure under changes of space and/or time scale. If the probability distribution function (PDF) of the fluctuations in rainfall Rl at some scale l is Pl(Rl), then the simplest form of scale invariance is if the PDF at a different scale l0 is given by Pl0 Rl0 H Pl H Rl 3 where l is the ratio of scales (l/l0 ) and H is a constant. That is, the PDFs at the two scales are identical except for a rescaling factor that depends on the ratio of scales. It is then straightforward to show that the moments of the rainfall fluctuations are then a power-law function of scale, i.e., h Rlj jq i / lqH 4 for order q. This can be tested on observed data in a reasonably straightforward manner. This stochastic self-similar model can be referred to as a fractal, or monofractal, model, since in the limit as l tends to zero it would produce a field of singularities with a single fractal dimension H. In reality, the model does not apply all the way down to infinitely small scales, but over a finite range of scales. Within this scaling range, the model of how the PDF varies with scale can be used to compare data between scales, to perform down- scaling or up-scaling, to simulate precipitation fields, or in data-merging applications. The model can also be extended to multiscaling, in which the moments of the fluctuations are still power-law functions of scale as in eqn [4], but instead of the exponents being a linear function of q, they are given by h Rlj jq i / ltq 5 where t(q) is a continuous concave function of the moment-order q. In this case, the PDF does not maintain its shape between two different scales, but changes continuously in a way that still depends only on the ratio of scales. In general, the smaller the scale, the fatter the tail of the distribution, i.e., as scale l ! 0 the higher moments increase rela- tively faster than the lower-order moments. This multiscaling model is consistent with the statistics resulting from a multiplicative cascade processes, in which the values of the field at smaller scales are produced by multiplying the field value at a larger scale by a stochastic weight variable, as shown in Figure 5. Multiplicative cascade models predict not only the one-point PDF of the rainfall fluctuations, but also the correlations between measurements made at dif- ferent locations as a function of measurement scale, and even the correlation between measurements at different locations and different scales. This structure can be used for multiscale objective analysis and interpolation between sparsely recorded data, or for merging measurements at different scales and locations. If there is a scale-invariant structure in both time and space, the time and space scaling can be com- bined into a single model, using a multiplicative fac- tor to transform the time dimension to an equivalent spatial dimension. If a single velocity U is used at all scales to transform from time-scale t to space-scale l, i.e., l Ut, then this is equivalent to Taylors frozen turbulence hypothesis. However, it is also possible to use a different factor at each scale and maintain the scale-invariant structure in both space and time, as long as the velocity is also a power-law function of scale, which gives t=t0 l=l0 z for constant expo- nent z. Then a single spacetime model of scaling can be constructed with time considered to be an extra spatial dimension. After almost two decades of examining measure- ments with different instruments, it has been shown, and is now generally accepted, that precipitation fields do indeed show scale-invariant behavior with multiscaling, at least over some range of spatial A completely uniform field After multiplication by 2 random factors After multiplication by 4 more random factors etc. =4 =2 =1 Figure 5 A schematic representation of the cascade process in one dimension, with shading used to represent the value of the scalar field. Each structure is broken up into two substructures, transferring some or all of its value to the substructures. This is modeled mathematically by multiplicative factors being applied at each level. The scale is labeled by the ratio = (maximum length)/(current grid size). Hydrology _ Atmospheric Water and Precipitation 65 and temporal scales. What is not so clear is what this range of spacetime scales is, or what the exact scaling exponents are, since the scaling range and scaling expo- nents vary between measurement instruments, and between different rainfall regimes and locations. This suggests that although the presence of (multi)scaling may be universal, the scaling range and parameters are dependent on the prevailing meteorological conditions, type of precipitation, and other local variables. Some research has been done along these lines: in 1996, Perica and Foufoula-Georgiou found that the scaling parameters for mid-latitude mesoscale convective sys- tems could be predicted by the convective available potential energy (CAPE) before the storm; and more recently some work has been done to relate the scaling statistics of orographic rainfall to the surface elevation driving the precipitation system. However, it still remains a challenge to determine the dependence of the scaling parameters and the scaling-range for precip- itation in different types of storms and different locations. Conclusions Precipitation is one of the most important links between weather and climate and the hydrological cycle, on time scales ranging from hours to decades or longer, and space scales from meters to hundreds or thousands of kilometers. Some of the most direct effects of climate change on humans are related to changes in the amount, or the distribution, of precipi- tation, including the distribution of extreme events. Many of the difficulties in modeling precipitation are the result of the spacetime structure and intermittency of the precipitation field, which are due to the fact that it is influenced by many dynamic processes that act on a large range of scales. However, the improved spatial resolution provided by the modern technologies of radar and satellite measurements has allowed progress in the physical modeling of precipitation, as well as the development of scale-invariant statistical models that can encompass that variability with a relatively small number of parameters. Some challenges that lie ahead are to find the range of scales and conditions to which both the physical and statistical models apply accu- rately, and to relate the statistical scaling parameters to environmental conditions for various types of precipi- tation. For numerical cloud models, despite the computational resources now available, which allow very high resolutions, research shows that ignoring small scale processes and variability (which for practi- cal purposes may not be of importance in themselves) leads to errors in larger-scales processes and quantities due to nonlinearities in the dynamics. Thus, cloud parameterizations and nested dynamically evolving grids that incorporate accurate subgrid statistics are active areas of research. Therefore, it seems that it would be of great benefit to incorporate research on statistical models with the numerical cloud resolving models, in an attempt to both improve the verisimili- tude of the numerical models in reproducing precipita- tion fields with the correct statistics, and to study the dependence of (multi)scaling models on different envi- ronmental parameters. Glossary Adiabatic lapse rate The rate of decrease in temper- ature with height for a parcel of air that does not exchange heat with the surrounding atmosphere i.e., that is assumed to be perfectly insulated. Cloud condensation nuclei (CCN) Aerosol particles suspended in the air on which water can condense. Cloud resolving model (CRM) Numerical model of the atmosphere that includes the modeling of cloud and precipitation processes. Fractal A geometrical object that is scale invariant, with structure at all scales and a simple one-parameter function to transform from one scale to another. Multifractal A generalization of the fractal to in- clude more variable fields, and allow more complex scaling behavior so that the transform from one scale to another is a function of more than one parameter in general a continuum of scaling exponents. Passive scalar A quantity or substance that is trans- ported by moving fluid without having any effect on the dynamics of the fluid. Also known as a tracer. Scale invariance The property of being self-similar under changes in spatial or temporal scale, so that the probability distributions or other relevant prop- erties of a field keep the same form (possibly with renormalization). Stratiform Forming a layer or arranged in layers. Used to refer to a broad class of clouds that form layers of large horizontal extent. See also: Evapotranspiration; Hydrological Cycle and Water Budgets; Physical Properties of Water; Vadose Water. 66 Hydrology _ Atmospheric Water and Precipitation Further Reading Antolik MS (2000) An overview of the National Weather Services Centralized Statistical Quantitative Precipitation Forecasts. Journal of Hydrology 239: 306337. Brutsaert W (2005) Hydrology: An Introduction. Cambridge: Cambridge University Press. Doviak RJ and Zrnic DS (1993) Doppler Radar and Weather Observations, 3rd edn. San Diego, CA: Academic Press. Droegemeier KK, Smith JD, Businger S, et al. (2000) Hydrological aspects of weather prediction and flood warnings: Report of the Ninth Prospectus Development Team of the U.S. Weather Re- search Program. Bulletin of the American Meteorological Society 81: 26652680. Foufoula-Georgiou E (1997) On scaling theories of spacetime rainfall: Some recent results and open problems. In: Gupta, et al. (eds.) Stochastic Methods in Hydrology: Rain, Landforms and Floods, pp. 2572. Singapore: Word Scientific. Foufoula-Georgiou E and Vuruputur V (2001) Patterns and orga- nization in precipitation. In: Grayson R and Bloschl G (eds.) Spatial Patterns in Catchment Hydrology Observations and Modeling, pp. 82104. New York: Cambridge University Press. Kidd C (2001) Satellite rainfall climatology: A review. International Journal of Climatology 21: 10411066. Kummerow C, Olson WS, and Giglio L (1996) A simplified scheme for obtaining precipitation and vertical hydrometeor profiles from passive microwave sensors. IEEE Transactions on Geosci- ence and Remote Sensing 34: 12131232. Randall DA, Khairoutdinov M, Arakawa A, and Grabowski W (2002) Breaking the cloud-parameterization deadlock. Bulletin of the American Meteorological Society 84: 15471564. Rasmussen EM and Arkin PA (1993) A global view of large-scale rainfall variability. Journal of Climate 6: 14951521. Veneziano D, Langousis A, and Furcolo D (2006) Multifractality and rainfall extremes: A review. Water Resources Research 42: W06D15,doi:10.1029/2005WR004716. Wallace JM and Hobbs PV (1977) Atmospheric science: an intro- ductory survey. New York: Academic Press. Relevant Websites National Weather Service. National Atmospheric and Oceanic Administration. Global Precipitation Measurement. Tropical Rainfall Measurement Mission. World Weather 2010 Project. Hydrology _ Atmospheric Water and Precipitation 67 Snow and Ice G Hornberger, Vanderbilt University, Nashville, TN, USA T C Winter, US Geological Survey, Denver, CO, USA 2009 Elsevier Inc. All rights reserved. The cryosphere is the portion of Earths surface where water exists in solid form. In the winter, snow covers more than 60% of the Northern Hemispheres land area whereas there is little snow cover in the South- ern Hemisphere except for Antarctica (UNEP/GRID- Arendal, 2007). Snow and ice cover about 10% of the land area permanently. Snow and ice (primarily gla- ciers and ice sheets) store large amounts of fresh water; most of the Earths fresh water resides in two major ice sheets, Greenland (area 1.75 106 km2 ) and Antarctica (area 12.1 106 km2 ). Snow and ice affect essentially all aspects of the hydrological cycle. Frozen ground reduces infiltration of water into soils and can increase the runoff gener- ated from melting snow. Permafrost severely reduces the amount of water that can be stored in soils. Sea- sonally and permanently frozen land surfaces interact significantly with the global weather and climate sys- tem, affecting surface albedo (i.e., the reflection of solar radiation) and latent energy exchanges (i.e., evaporation). Earths glaciers and ice caps have been undergoing significant recession, with measurable impacts on sea level, water resources, and ecosystems. The state of the cryosphere, which has been cited as having a unique sensitivity to climate change at all spatial and temporal scales (Slaymaker and Kelly, 2007), is viewed as an important indicator of climate change. The melting of snow and ice has substantial effects on inland waters. Seasonal snow cover in many mountainous regions is of critical importance to water supply. The melting of snow and ice can affect hydrological processes and their linkages with ecosys- tems. Streams swollen by snow and ice melt in the spring can (1) scour streambeds and deposit new sand bars, resulting in new substrate for benthic and other organisms that rely on the changing geomorphic and fluvial conditions, and (2) overtop stream banks, depositing fresh sediments and providing water for riparian and floodplain wetlands. The melting of snow and glaciers in high mountains can sustain alpine lakes and wetlands as well as supply water to streams throughout summer. This relatively reliable source of water sustains both aquatic and terrestrial alpine ecosystems as well as riverine ecosystems asso- ciated with the ice-melt-sustained river flows. Further Reading Slaymaker O and Kelly R (2007) The Cryosphere and Global Environmental Change. Blackwell. UNEP/GRID-Arendal. Cryospherewinter seasons, Northern and Southern Hemispheres [Internet]. UNEP/GRID-Arendal Maps and Graphics Library; June 2007 [cited 2007 Nov 26]. Avail- able at northern-and-southern-hemispheres. Relevant Websites Arctic Climate Im- pact Assessment (especially Chapter 6, Cryosphere and Hydrol- ogy). National Snow and Ice Data Center. 68 Evapotranspiration G Katul and K Novick, Duke University, Durham, NC, USA 2009 Elsevier Inc. All rights reserved. Introduction Earths water is highly dynamic and continuously in motion, and the terms water cycle or hydrologic cycle describe the continuous movement of water molecules on, above, and below the surface of the Earth. The water cycle concept may be traced back to the Greeks, evidenced for example in the Iliad (written around 800 BC), when Homer described the oceans from whose deeps every river and sea, every spring and well flows. . . suggesting intercon- nectedness of all of the Earths water. Leonardos Codex Leicester, written between 1506 and 1510, was a seminal document mostly focused on water, and also advanced the concept of a large-scale water cycle by offering keen observations on the dynamics and transport of water (and suspended particles) by streams and rivers originating in the mountains and continuing through the plains to the sea. More impor- tantly, the Codex Leicester is one of the first Albums of Fluid Motion or flow visualization studies, dis- cussing many aspects of the hydrologic cycle and its connection to fossils, geology, and climate. Because of its intrinsic role in the hydrologic cycle, the study of evapotranspiration (ET), the sum of evap- oration (E) and plant transpiration (T), has a rich research history, and to discuss every nuance of the topic is beyond the scope of a single chapter. The focus here is on ET, the engine of the hydrologic cycle, crucial for determining usable water for humans and ecosystems. We explore how the projected climatic and land cover changes might alter ET over a hierarchy of scales ranging from global to continental to local. Throughout, E here refers to the movement of water to the atmosphere from sources such as the soil matrix, rainfall intercepted by plant canopies, and water bod- ies, while T refers to the loss of water in the form of vapor molecules passing through leaf stomata. The first attempt to quantify the role of ET in the hydrologic budget is often attributed to John Dalton, who carried out the necessary calculations to con- struct hydrological balances of major rivers (includ- ing the Thames), and published them in 1802 in the manuscript titled Experiments and observations to determine whether the quantity of rain and dew is equal to the quantity of water carried off by the rivers and raised by evaporation; with an inquiry into the origin of springs. Dalton is also known for his work on partial pressures, which lead to the first physically based quantitative model of evaporation (see Box 1). In the next section, it is demonstrated that Daltons seminal work, along with others in the nineteenth century, lead to developments of quantitative laws for E that find wide use today in constraining esti- mates of the acceleration of the hydrologic cycle because of projected increases in global air tempera- ture. The term acceleration of the hydrologic cycle refers to the fact that higher temperatures provide more kinetic energy to water molecules, leading to more evaporation and thus more precipitation. Evaporation and the Projected Acceleration in the Global Hydrologic Cycle It is now accepted that increases in greenhouse gas emissions lead to increases in air temperature. How- ever, the effects on the hydrologic cycle are far more difficult to predict. It is appropriate to start with a first-order estimate of how much the global hydrologic cycle is expected to accelerate following an increase in global air temperature (dTa) using only the nine- teenth century equations presented by John Dalton, Rudolf Clausius, and Benoit Paul Emile Clapeyron (see Box 1). From Box 1, it can be shown that the combination of these nineteenth century laws lead to dP P dE E 0:0675dTa where dP and dE are projected changes in global rain- fall and global evaporation in response to dTa, respec- tively. On the basis of the nineteenth century laws, a 1 C warming (roughly commensurate with the warm- ing trend experienced over the past century, which is estimated at 0.15 C per decade) leads to a 6.8% increase in global rainfall (or E). Furthermore, a 4 C projected warming trend, predicted to result from a doubling in atmospheric CO2 concentration, can produce up to a 27% increase in rainfall (or E). These calculations may be compared with contempo- rary estimates obtained using the state-of-the-art high- resolution climate models that couple oceanic and atmospheric circulation (and stretch the best currently available supercomputing facilities) that predict dP P 0:035dTa 1:4 This modern estimate suggests that a 4 C projected warming will result in about 9% increase in rainfall. 69 Note that this dP differs from the estimate in Box 1 in slope (by about a factor of 2), and by the offset of 1.4 K that can be attributed to thermal inertia in the Earth system (i.e., some finite warming is necessary before the hydrologic cycle begins to be impacted). The differ- ences in the slopes between these two estimates can be traced back to inefficiencies in the hydrologic cycle that are accounted for in climate models, as well as the many feedbacks not accounted for in the calcula- tions shown in Box 1. Examples of such feedbacks include the formation of clouds in advance of rainfall, which block direct sunlight from arriving at the surface and reduce bulk conductance, thereby decreasing ET. Hence, according to Box 1, the projected acceleration in the global hydrologic cycle is primarily due to a global increase in ET, and nineteenth century laws provide a reasonable upper limit to constrain its value. Evapotranspiration and the Continental-Scale Hydrologic Cycle The problem of assessing how climatic changes prop- agate through various terms in the continental-scale hydrologic balance is complicated, than in the global case, by the addition of a new term continental-scale runoff (Ro). Over long periods of time, the continen- tal-scale hydrologic balance can be expressed as p ET R0 Nearly all studies investigating continental-scale trends in ET over the past 50100 years suggest some change has occurred, but conflicting conclu- sions persist about the direction of this change. While continental-scale ET may be an order of magnitude smaller than oceanic E, replenishment of most water resources and ecosystem goods and ser- vices, as well as delivery of essential nutrients to marine estuaries, depends on the continental-scale R0. The arguments presented in Box 1 suggest an increase in ET in a warmer climate, but a number of studies have documented an increase in continental- scale runoff in recent years. Hence, how ET may have changed over the past 50100 years appears to be controversial, and reconstructing how continental- scale ET changed over the past 100 years is a logical test of current skills in predicting the future of the hydrologic cycle. Three hypotheses have been promoted as plausi- ble explanations for a decreasing ET over the past 50100 years, each with certain limitations. The first is the so-called solar dimming hypothesis. This hypothesis argues that a reduction in solar irradiance occurred because of an increase in cloud cover and aerosols concentration, the latter being consistent with measured increases in air pollution throughout the past 100 years (Table 1). Solar irradiance is a key forcing for the available energy that drives ET and influences bulk conductance through the effect of light on leaf photosynthesis (see Box 2). The decrease in pan evaporation rate measured over the last 50 years over much of the conterminous United States and Russia is used as indirect support for this hypoth- esis. A pan evaporameter is a simple device consisting of a cylindrical container about 1.2 m in diameter and 0.25 m deep filled with water, a water level measur- ing device, and a rain gage. Naturally, pan evapora- tion is influenced by complex micrometeorological Box 1 Acceleration of the Global Hydrologic Cycle with Increased Temperature A Scaling Analysis Using Nineteenth Century Formulations A first-order estimate of the acceleration in the hydrologic cycle in response to a global increase in air temperature (dTa) is carried out using physical laws (in boxed quantities) derived by the nineteenth century scientists John Dalton, Rudolf Clausius, and Benoit Paul Emile Clapeyron. At the global scale, once sufficiently long periods of time have elapsed (e.g., decades or longer) it is safe to state that the global hydrologic balance can be reduced to P % E, where P is the global rainfall. Hence, any change in the global hydrological cycle due to an increase in air temperature must affect both rainfall and evaporation expressed as dP P dE E where dP and dE are changes in global rainfall and global evaporation due to a dTa. Using Daltons law, E % gw D where gw is referred to as the conductance of the surface to water vapor, and D is the vapor pressure deficit defined as e*(Ta) (1 RH), where e* is the saturation vapor pressure at Ta and RH is the global air relative humidity. The ClausiusClapeyron equa- tion can now be used to relate e* to Ta using, e Ta a exp bTa Ta c 8 >: 9 >; where Ta is the temperature ( C), a 0.611 kPa, b 17.5 C1 , and c 249.93 C for typical atmospheric pressures. In existing climate simulations, the effects of increased greenhouse gases on dTa do not lead to appreciable changes in RH, even across a wide range of climate scenarios. Hence, in a first-order analysis, assuming that RH maintains its present global value, we find that dP P dE E dD D de Ta eTa bTa c Ta2 b c Ta 8 >>>: 9 >>>;dTa An order of magnitude analysis demonstrates that bTa cTa 2 ( b cTa 8 : 9 ; resulting in dP P b c Ta dTa Using the current global air temperature Ta = 15 C, and sub- stituting b 17.5 C1 , and c = 249.93 C results in dP P dE E 0:0675dTa 70 Hydrology _ Evapotranspiration processes like local wind flow and is often used as one indicator of potential ET. Pan evaporation records are amongst the longest available hydrologic records, spanning some 100 years in several locations. Some studies estimate that the measured reduction in pan evaporation is consistent with solar dimming rates of 24% per decade. The 24% per decade range was independently confirmed from observation for the period between 1960 to late 1980s, using the Baseline Surface Radiation Network (BSRN) of the World Climate Research Program (WCRP). However, solar dimming now appears to be giving way to the so-called solar brightening at a rate of about 1.6% per decade (Table 1). This brightening is partly explained by the recovery from the large aerosol loadings associated with the 1991 Pinatubo eruption, and a decline in Eastern European aerosol emissions due to tighter air-quality regulations in those regions. Other authors question this continental view of dimming and favor local-scale explanations. These studies reported that dimming was four times more frequently observed near population centers (defined as centers with a population size exceeding 0.1 mil- lion) than in sparsely populated areas. Irrespective of whether solar dimming, brighten- ing, or even flickering will be the scenario for the future, the contention that a reduction in pan evapora- tion can be correlated with actual reductions in ET is not universally accepted. The so-called complementary hypothesis argues that a reduction in pan evaporation actually corresponds to an increase in ET, particularly in water-limited ecosystems. This hypothesis is based on the prediction that higher ET increases humidity, cools the air, and reduces the vapor pressure deficit (D), thereby reducing potential (or pan) evaporation. Climatological studies across the conterminous United States suggest that D did not significantly increase over the past 50 years despite a decline in the pan evapora- tion record, thereby negating one of the assumptions of the complementary hypothesis. However, analysis of published precipitation and stream discharge data for several large basins across the conterminous United States show that ET rates, estimated as the difference between rainfall and runoff, have increased over the past 50 years. It is clear that further studies are neces- sary to resolve how the pan evaporation record needs to be interpreted and whether it can be used in a complementary formulation for actual ET. The second hypothesis, promoted by sensitivity stud- ies conducted using climate models, was aimed at exploring why continental-scale runoff increased in the past 50100 years. This hypothesis argues that a reduction in stomatal conductance should occur following the 100 ppm increase in global atmospheric CO2 concentration over the past 100 years (see Box 2). The response of plant stomata to elevated atmospheric CO2 has been studied for over 30 years now and some experiments support a decrease of up to 50% with doubling of atmospheric CO2. When such stomatal Box 2 Changes in Continental-Scale ET Extending Daltons law to ET (see Box 1), ET % gc D where now gc is the bulk conductance of the soilplant system (i.e., it lumps conductances in the soil and plant). Hence, dET ET dD D dgc gc Any solar dimming, increased atmospheric CO2 and its con- comitant effect on bulk stomatal conductance, and the overall increase in global deforestation all are viewed as factors leading to a negative dgc/gc that is greater than any expected increases in dD/D with warming (see Box 1), resulting in a decline in dET/ ET over continents. The basic challenge confronting the scien- tific community today in quantifying dgc/gc over continents is that the relationships between gc, light levels, atmospheric CO2, soil moisture, and species composition are nonlinear and vary considerably across biomes, soil type, etc. When quantifying dgc/gc, it is convenient to explore the indi- vidual conductances (i.e., stomatal and soil conductances) sep- arately because they respond differently to environmental drivers, particularly elevated atmospheric CO2. Table 1 Observed global changes in radiation Dates of measurements Observed change in radiation Source 19581992 0.51 W m2 yr1 0.41 W m2 yr1 in densely populated areas, 1 19641980 2 0.16 W m2 yr1 in sparsely populated areas 19842001 0.24 W m2 yr1 4, 5 19922002 0.66 W m2 yr1 6 Sources 1. Stanhill G and Cohen S (2001) Global dimming: A review of the evidence for a widespread and significant reduction in global radiation with dis- cussion of its probably causes and possible agricultural consequences. Agricultural and Forest Meteorology 107: 225278. 2. Alpert P, Kishca P, Kauffman YJ, and Schwarzbard R (2005) Global dimming or local dimming?: Effect of urbanization on sunlight availabil- ity. Geophysical Research Letters 32: Art. No. L17802. 3. Roderick ML (2006) The ever-flickering light. Trends in Ecology and Evolution 21: 35. 4. Pinker RT, Zhang B, and Dutton EG (2005) Do satellites detect trends in surface solar radiation? Science 308: 850854. 5. Wild M, Gilgen H, Roesch A, Ohmura A, Long CN, Dutton EG, Forgan B, Kallis A, Russak V, and Tsvetkov A (2005) From dimming to brightening: Decadal changes in solar radiation at Earths surface. Science 308: 847850. Hydrology _ Evapotranspiration 71 conductance reduction functions are directly incor- porated into land-surface models embedded within the larger climate models, ET significantly declined and global runoff increased to levels consistent with runoff observations. These climate models are now routinely used as earth simulators for addressing potential CO2-induced interactions between terrestrial ecosystemsandclimate.However,thesesignificantcon- ductance reduction explanation due to elevated atmo- spheric CO2 are not entirely supported by recent results from Free Air CO2 Enrichment (FACE) experiments, which are designed to investigate how elevated atmo- spheric CO2 affects both leaf and whole-ecosystem biosphereatmosphere exchange rates. Several studies have explored how leaf stomatal characteristics are altered by elevated atmospheric CO2 (Table 2). In par- ticular, these studies examined the phenotypic response of stomatal index (SI), stomatal density (SD), and sto- matal aperture (AP) to rising atmospheric CO2 in 15 species after 4 years exposure to a field CO2 gradient (200550 ppm) or within three FACE sites. Along the CO2 gradient experiments, SI and SD showed no evidence of a decline to increasing CO2, while AP decreased slightly. It appears that without evolutionary changes, SI and SD may not respond to atmospheric CO2 in the field and are unlikely to decrease in future climates characterized by high CO2. The third hypothesis argues that the decrease in continental-scale ET over the past 100 years is related to the large-scale land-use change, with defor- estation being the dominant trend. It is well known that clearing forests for development or agricultural purposes decreases ET and thus increases surface runoff. Direct experimental evidence of the impact of land cover conversion on ET was explored from long-term eddy-covariance measurements carried out at the Duke Forest, near Durham, North Carolina, at three stands experiencing similar climatic and edaphic conditions (Figure 1, Table 2). These measure- ments demonstrate that the difference between P (same for all sites) and ET is smallest for a pine plantation (PP), followed by the second-growth mixed hardwood forest (HW), followed by an abandoned agricultural field (OF) that is harvested at least once annually to prevent woody encroachment (Figure 2). Interestingly, the maximum difference in P ET for this experiment was 180 mm year1 over this 5-year period here, which is comparable with the reported globally averaged decrease in streamflow following the afforestation of grasslands, shrublands, or croplands (227 mm Table 2 Reported changes in E, T, and related variables and their attributed causes Scale of study Region of study Variable(s) of interest Change in variable(s) Proposed cause of change Source Continental United States Pan evaporation 90150 mm yr1 from 1960 to 1990 Solar dimming 1 Continental United States Pan evaporation/E 110 mm yr1 /No trend from 1960 to 1990 Complementary hypothesis 2 Ecosystem Eastern TN E/T/gs/gc No Change/10%/44%/14% Elevated CO2 3 Ecosystem Central NC T/gc 4%/No change Elevated CO2 4 Global Global gs 27% to 40% in herbaceous plants Elevated CO2 5 Ecosystem NC, TN, NV SI, SD, AP No change/no change/slight decrease Elevated CO2 6 Global Global Ro 227 mm yr1 in afforested watersheds Land-use change 7 Ecosystem Central NC E/T 28%/58% Conversion from a grass field to a PP 8 Sources 1. Roderick ML and Farquhar GD (2002) The cause of decreased pan evaporation over the past 50 years. Science 298: 14101411. 2. Golubev VS, Lawrinmore JH, Groisman PY, Speranskaya NA, Zharavin SA, Menne MJ, Peterson TC, and Malone RW (2001) Evaporation changes over the contiguous United States and the former USSR: A reassessment. Geophysical Research Letters 28: 26652668. 3. Wullschleger SD, Gunderson CA, Hanson PJ, Wilson KB, and Norby RJ (2002) Sensitivity of stomatal and canopy conductance to elevated CO2 concentration Interacting variables and perspectives of scale. New Phytologist 153: 485496. 4. Schafer KVR, Oren R, Lai C-T, and Katul GG (2002) Hydrologic balance in an intact temperate forest ecosystem under ambient and elevated atmospheric CO2 concentration. Global Change Biology 8: 895911. 5. Field CB, Jackson RB, and Mooney HA (1995) Stomatal responses to increased CO2Implications from the plant to the global scale. Plant Cell and Environment 18: 12141225. 6. Reid CD, Maherali, H, Johnson HB, Smith SD, Wullschleger SD, and Jackson RB (2003) On the relationship between stomatal characters and atmospheric CO2. Geophysical Research Letters 30: 19831986. 7. Jackson RB, Jobbagy EG, Avissar R, Roy SB, Barrett DJ, Cook CW, Farley KA, le Maitre DC, McCarl BA, and Murray BC (2005) Trading water for carbon with biological sequestration. Science 310: 19441947. 8. Stoy PC, Katul GG, Siqueira MBS, Juang J-Y, Novick KA, McCarthy HR, Oishi AC, Uebelherr JM, Kim, HS, and Oren, R (2006) Separating the effects of climate and vegetation on evapotranspiration along a successional chronosequence in the southeastern U.S. Global Change Biology 12: 21152135. TN, NC, and NV refer to the states of Tennessee, North Carolina, and Nevada, respectively. 72 Hydrology _ Evapotranspiration year1 globally, or $38% on average). Note that this reduction in ET due to land cover conversion from PP to OF is on the order of 20%, which is much larger than the 6.8% increase in dD/D resulting from a 1 C warm- ing (see Box 1). Evapotranspiration at Local Scales: Knowledge Gaps and Why the Problem of its Quantification Persists Why does ET, studied for over thousands of years, still pose unique challenges to contemporary hydrologists? The answer may lie in the basic laws that describe water movement from the soil to the atmosphere. Movement of water in the soilplantatmosphere system begins with water migrating from wetter to drier soil pores adjacent to the root system moving along potential energy gradients. Once water reaches and enters the root system through a patchy and heterogeneous root-membrane, water flows through Figure 1 Experimental setup for the afforestation experiment at the Blackwood Division of the Duke Forest, near Durham, North Carolina showing the tower location at the grass site (OF), pine site (PP), and hardwood site (HW). 1500 1000 500 mmPET(mm) 1998 1999 2000 2001 2002 2003 2004 2005 OF PP HW P 2006 1998 1999 2000 2001 2002 Year 2003 2004 2005 2006 0 800 600 400 200 0 200 Figure 2 Top: Variations in eddy-covariance measured cumulative ET and P for the old-field (OF), pine plantation (PP), and hardwood forest (HW). Bottom: For reference, P ET, a surrogate for water availability, is also shown. Hydrology _ Evapotranspiration 73 a tortuous and complex network within the xylem. It experiences phase transition within the leaves, and exits to the atmosphere in the form of water vapor through patchy leaf stomata. The vapor molecules are then transported by turbulent eddies from within the canopy into the free atmosphere. The transporting energy and sizes of these eddies are partially deter- mined by complex interactions among canopy attri- butes (e.g., leaf area and height), mesoscale forcing (e.g., geostrophic winds and weather patterns), and landscape heterogeneity. Resolving all spatial scales needed to describe the trajectory of water in the soilplantatmosphere system necessitates a three- dimensional simulation domain spanning 0.1mm to tens of kilometers, equivalent to requiring $(1010 )3 computational nodes per time step. This time step must be sufficiently fine to resolve the fastest process, which is the action of viscous dissipation on turbulent fluctuations in the atmosphere ($0.001 s). This high dimensionality in space and time is well beyond the capacity of any brute-force computation at present and in the foreseeable future. Furthermore, there are numerous insurmountable scale issues in attempting to relate water flow in the soilplant system with its driving forces. For one, the constitutive laws now used to describe water movement in the soil, root, plant, and atmosphere systems do not share the same representative elementary volume (REV), defined here as the minimal spatial scale of representation for these laws. To elaborate further on these laws, we consider each of them separately for the three compartments of the soilplantatmosphere system: 1. Soil: Darcys law, first proposed in 1856 and considered as one of the hallmarks of nineteenth century Earth sciences, describes the water flux, and when combined with the soil moisture conservation of mass equation (referred to as the continuity equation), leads to the so-called Richards equation. This equation describes water movement in unsaturated soils near the rooting- zone at an REV scale containing a sufficiently large number of pore spaces. Richardss equation is a nonlinear partial differential equation that provides a spacetime description of water move- ment, but averages out variability of soil and root matrices at scales smaller than its REV. In soil physics, one of the major theoretical challenges to upscale this equation beyond the REV is how to include the effects of spatial heterogeneities in soil properties, macroporosity, and preferential flows of water and nutrient at discontinuities (e.g., large roots). Even the application of Darcys law within the REV of a soilsystem punctuated by complex rooting remains questionable. It is clear that the laws that describe water movement from the soil pores up to the rooting zone, proposed some 150 years ago, remain approximate. 2. Plant: Analogous problems arise at the plant level when describing water movement from the root to the leaf. Laminar flow equations (e.g., Hagen Poiseulles law for capillary tubes), based on the continuum assumption in fluid mechanics, are typically used to describe root and xylem water movement(orvelocities).Theseassumptionsarenow being challenged by recent research in plant hydrau- lics. Forexample, prediction of the onset of embolism (cavitation) in the plant xylem requires microscale thermodynamic description of air and water micro- fluid dynamics not captured by macroscopic flow equations such as Poiseulles law. The derivation of empirically measured embolism vulnerability curves for various plant organs from first principles has not yet been rigorously tackled and remains a topic of active research. Even the precise hydraulic pathways and connections between stomatal conductance and the plantxylem system remain a subject of research awaiting novel experiments and theories. 3. Atmosphere: For the free atmosphere, being a single medium, the physical laws for mass, momentum, and energy exchanges are well described by the so-called NavierStokes equations, yet another hallmark of nineteenth century science. These are a set of nonlinear partial differential equations that are often described as the last frontier in classi- cal mechanics. They require detailed description of boundary conditions at the plantatmosphere interface. Describing the boundary conditions for these equationsremainscomplicatedbystochasticity in the geometry and evolution at multiple scales. Randomness, beginning with patchiness at the stomatal level and progressing to patchiness in stomatal conductance, random leaf distribution, leaf area density, and onwards to the atmosphere must all be accounted for as dynamic boundary conditions. This boundary condition complexity does not diminish the complexity of solving these equations even for simple static boundary condi- tions.TheNavierStokesequationscannotbesolved at all the necessary scales except in idealized cases. Evenwhentheseconstitutiveequations(Richardsequa- tion, Poiseuille law, and NavierStokes equations) provide reasonable approximations at a particular scale, typically where microscopic heterogeneities can be averaged out within their respective REV, a major challenge remains in the derivation of effective para- meters for simplified models at larger scales needed for addressing questions pertinent to the global and regional water cycle. 74 Hydrology _ Evapotranspiration Conclusions The importance of ET in sustaining the global and continental hydrologic cycle and the worlds freshwa- ter resources is rarely questioned in hydrology, mete- orology, ecology, and soil science. Nonetheless, much uncertainty remains regarding the magnitude, and even the direction, of trends in continental-scale ET in the present day and over the course of the next century. Both state-of-the-art climate models and the- oretical work indicate that global ET should increase in a warmer climate. Nonetheless, observational studies suggests that continental-scale ET may be increasing or decreasing as a result of a combination of forcings including warmer temperatures, decreased bulk conductance associated with rising CO2 concen- trations, and large-scale land-use change. Attempts to resolve this uncertainty are challenged by the difficulty in integrating microscale processes, including water transport through soil pores and plant xylem, into a framework that can describe regional- and continental-scale patterns of ET. Constitutive laws such as Richards equation, Poiseulles law, and the NavierStokes equations can describe water movement through soil, plants, and the atmosphere, respectively, under some circumstances. However, even these nineteenth century based hallmark equa- tions, when applied to continental scales, challenge the computational limits. Given that the majority of fresh water available for use by both humans and ecosystems is governed by the difference between P and ET on regional to continental scales, it should be clear after this review that novel theoretical tactics are needed to further the development of these consti- tutive laws and their upscaling for ET applications. Acknowledgments This study was supported by the US Department of Energy (DOE) through the Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes (TCP) program (Grant nos. 105090152, DE-FG0200ER53015, and DE-FG0295ER62083), and by the National Science Foundation (NSF-EAR 0628342 and NSF-EAR 0635787). Further Reading Allen MR and Ingram WJ (2002) Constraints on future changes in climate and the hydrological cycle. Nature 419: 224232. Brutsaert W (1982) Evaporation in the Atmosphere: Theory, His- tory, and Applications 299. Kluwer Academic Publishers. Brutsaert Wand Parlange MB (1998) Hydrologic cycle explains the evaporation paradox. Nature 396: 30. Campbell GS and Norman JM (1998) An Introduction to Environ- mental Biophysics, pp. 286. Springer-Verlag. Cox PM, Betts RA, Jones CD, Spall SA, and Totterdell IJ (2000) Acceleration of global warming due to carbon-cycle feedbacks in a coupled climate system. Nature 408: 184187. Easterling DR, Meehl GA, Parmesan C, Changnon SA, Karl TR, and Mearns LO (2000) Climate extremes: Observations, model- ing, and impacts. Science 289: 20682074. Gu L, Baldocchi DD, Wofsy SC, Munger JW, Michalsky JJ, Urbanski SP, and Boden TA (2003) Response of a deciduous forest to the Mount Pinatubo eruption: Enhanced photosynthe- sis. Science 299: 20352038. Jury WA, Gardner WR, and Gardner WH (1991) Soil Physics, pp. 328. Wiley. Katul GG, Porporato A, and Oren R (2007) Stochastic dynamics of plantwater interactions. Annual Review of Ecology, Evolution, and Systematics 38: 767791. Milly PCD, Dunne KA, and Veccia AV (2005) Global pattern of trends in streamflow and water availability in a changing cli- mate. Nature 438: 347350. Parlange MB, Eichingwer WE, and Albertson JD (1995) Regional- scale evaporation and the atmospheric boundary layer. Review of Geophyics 33: 99124. Peterson TC, Golubev VS, and Grolsman PYa (1995) Evaporation losing its strength. Nature 377: 687688. Ramanathatn V, Crutzen PJ, Kiehl JT, and Rosenfeld D (2001) Aerosols, climate and the hydrological cycle. Science 294: 21192124. Walter MT, Wilks DS, Parlange JY, and Schneider RL (2004) In- creasing evapotranspiration from the Coterminous United States. Journal of Hydrometeorology 5: 405408. Hydrology _ Evapotranspiration 75 Vadose Water J R Nimmo, U.S. Geological Survey, Menlo Park, CA, USA Published by Elsevier Inc. Introduction The term vadose is derived from the Latin vadosus, meaning shallow. In this sense, however, it refers to shallow depths beneath the land surface, not shallow portions of surface water bodies. The vadose zone is frequently called the unsaturated zone, and some- times the zone of aeration, as its pore space usually contains air as well as water. The vadose zone extends from the land surface to the water table (the lowest water table if there is more than one). Prediction of the transport rates of water and other substances within the vadose zone is critical to infil- tration, runoff, erosion, plant growth, microbiota, contaminant transport, aquifer recharge, and dis- charge to surface water. Vadose-zone flow is funda- mentally complicated by nonlinearity and hysteresis of unsaturated hydraulic properties, and extreme sen- sitivity to materials and hydraulic conditions. There is much variety in its natural constituents: soils, rocks, water, air, plants, animals, and microorganisms. Mod- ern hydrology must consider interactions not only among these constituents themselves, but also with a wide variety of contaminants, including pesti- cides, fertilizers, irrigation wastewater, manure, sew- age, toxic chemicals, radioactive substances, bacteria, mine wastes, and organic liquids. The porous medium of the vadose zone is typically soil (Figure 1), but may also be porous rock, or any other material that occurs near the earths surface. In general, the forces of molecular attraction are greater between solid and water than between solid and air. Consequently, water behaves as the wetting phase, and air as the nonwetting phase. Within the pores, water tends to cling to solid surfaces in films and in partially filled pores with curved airwater interfaces (Figure 2). Fundamental Processes of Vadose Water Unsaturated Hydrostatics Water content The most basic measure of the water is volumetric water content, often symbolized y, defined as the volume of water per bulk volume of the medium. The most standard measurement of y is the gravi- metric method. The procedure is to dry a sample of the porous medium in an oven until the weight is constant, and then calculate how much water was in the soil from the difference between the dry weight and the initial wet weight. Other methods in wide- spread use have advantages, such as being less disrup- tive. Neutron scattering is commonly used for monitoring y as a function of depth in the field. This method is based on the high effectiveness of water, among the various components of the wet soil, in slowing neutrons. Commercially available equipment has a neutron source and detector housed in a cylin- drical probe that can be lowered to various depths in a lined hole. Another way to monitor y in the lab or field is by measurement of the dielectric constant of the medium, usually by time-domain reflectometry (TDR). For most applications, TDR electrodes in the form of metal rods are inserted into the soil. Liquid water has a much higher dielectric constant than do other vadose zone constituents, so a measure- ment of this property can indicate the amount of water present within the volume sensed. A less com- mon method is to measure electrical conductivity, which increases with y. This principle can be ap- plied tomographically for observing two- or three- dimensional details of changing water distributions in the field. The reflective or absorptive behavior of ground penetrating radar can also be used di- rectly or tomographically to indicate water content distributions. Water pressure and energy Matric pressure, usually symbolized c, may be thought of as the pressure of the water in a pore of the medium relative to the pressure of the air, in other words, the pressure differ- ence across an airwater interface. The liquidsolid attraction that curves the airwater interfaces also causes capillary rise (Figure 3). Water that has risen to higher levels in the tube, because of the attraction of the tube walls for water, is at a lower pressure than the bulk water outside the tube. The narrower the tube, the stronger is the capillary effect. Similarly, in an unsaturated porous medium, water is generally at lower pressure than the air, so c is negative, the concave side of airwater interfaces is toward the air. The most direct measurement of c is by a tensiom- eter. In firm contact with the porous medium, this device allows for equilibration of pressure between the water in unsaturated pores and the water in a 76 small chamber where a gauge or transducer reads the pressure (Figure 4). Its use is limited to relatively wet soils. Other methods are available for relatively dry media and for easier application when less accuracy is accept- able. Some of these are based on the humidity of the air in soil pores. A low (strongly negative) c increases the pore waters effectiveness for absorbing water mole- cules out of the vapor in the soil air, resulting in a lower relative humidity. The effect is slight, however; a 0 to 15 atm range in c corresponds to a 100 to 99% range in relative humidity. Another class of methods uses an intermediary porous medium of known retention properties, typically gypsum blocks, nylon fabric, or filter paper. This medium is placed in contact with the medium to be measured so that c becomes equal in both. Then the water content of the intermediary medium is measured by other means (usually electrical conductivity, thermal diffusivity, or mass) and translated into a matric pressure using the known properties. Water retention Analogously to capillary rise, the smaller pores of a medium hold water more strongly than the larger pores do. To extract water from a h r Capillary tube Water Figure 3 Capillary rise in a tube. 100 m Figure 1 Particles and pores of a silt loam soil, scanning electron micrograph of a thin section. Reproduced from Lebron I, Schaap MG and Suarez DL (1999) Saturated hydraulic conductivity prediction from microscopic pore geometry measurements and neural network analysis. Water Resources Research 35: 31493158, with permission from the American Geophysical Union ( Water Air Mineral Figure 2 Pore space of a hypothetical unsaturated medium, illustrating the arrangement of solid, liquid, and gaseous phases. Few intergrain contacts appear in these figures because such contacts are essentially points in three-dimensional space, and mostly do not lie in the two-dimensional plane of the image. Hydrology _ Vadose Water 77 small pore requires application of a more highly neg- ative matric pressure. The volume of water held in the soil at different matric pressures therefore depends on the pore-size distribution, and is a characteristic of a particular porous material. This property, known as soilwater retention, is expressible as a set of y vs. c curves for a given medium. When c is close to zero, airwater interfaces are broadly curved, nearly all pores are filled, and y is high. If c is much less than zero, the interfaces are more tightly curved, they can no longer span the largest pores, and the pores have less water in them. Thus, greater y goes with greater (less strongly negative) c. Normally, during the process of wetting a porous medium, some air is trapped as the pores surrounding it become water-filled. In soil brought to c 0, it is common for trapped air to occupy one-tenth or more of the total pore space. Trapped air will eventually dissolve and diffuse away, but vadose-zone moisture conditions commonly change rapidly enough that the pore space always contains some amount of air. Consequently, for most retention curves, when c 0, y has a value less than the total porosity. In a granular medium, the particle-size distribu- tion, or texture, relates in some way to the pore-size distribution. Larger particles may have larger pores between them. In addition to texture, the structure of the medium, especially as related to such features as aggregation, shrinkage cracks, and biologically generated holes, substantially influences the retention curve. Examples Figure 5(a) shows a retention curve for a core sample of a silt loam soil from an apple orchard. Water retention is hysteretic; y for a given c is different when measured for drying and wetting, and in general depends on the wetting/drying history of the medium. Thus, there is not a unique curve but a family of curves. The drying retention curve in Figure 5(b) is far from linear and covers five orders of magnitude in c. This enormous range requires multiple measurement techniques. In most cases in- vestigators measure and plot only a single curve from the family of possible curves, usually a drying curve, and over only a portion of the range, usually at the wet end. 0.45 0.40 0.35 (a) (b) 0.30 0.25 0.20 0.15 0.10 0.05 0.0 106 104 102 100 40 20 Matric pressure (kPa) Water retention for sandy soil Matric pressure (kPa) Volumetricwatercontent Plano silt loam core sample Watercontent(vol/vol) 0 Pressure plate Water-activity meter Figure 5 Water retention relations. (a) Hysteretic water retention of a silt loam soil, with arrows indicating the direction of change on each curve. Reproduced from Nimmo JR and Miller EE (1986) The temperature dependence of isothermal moisture vs. potential characteristic of soils. Soil Science Society of America Journal 50: 11051113, with permission from the Soil Science Society of America. (b) Drying retention curve for a sandy soil from the Amargosa Desert Research Site. The points are measurements by two different methods and the smooth curve is a fit of the model of Rossi and Nimmo (1994). Reproduced from Andraski BJ (1996) Properties and variability of soil and trench fill at an arid waste-burial site. Soil Science Society of America Journal 60: 5466, with permission from the Soil Science Society of America. Pressure-measuring device Water-filled tube Soil Porous membrane Very fine water-filled pores Figure 4 A tensiometer establishes a continuous water phase from the soil pores to a chamber for pressure is measured to indicate matric pressure. 78 Hydrology _ Vadose Water Considering the drying of soil from saturation, y in Figure 5(b) stays high until a particular c value where it starts to decline. That c is called the air-entry value. By the capillary hypothesis, it is assumed to have a nonzero value because the largest fully wet pore of the medium will stay filled until the airwater pres- sure difference exceeds in magnitude the equivalent c value of capillary rise. In natural media, the air-entry value is usually poorly determined, as the decline in y with c starts gradually, beginning at c nearly equal to zero. Artificial porous media, however, can be made in such a way that many pores are close to the size of the largest pore, so that air-entry is a sharp and sudden phenomenon. Practical significance The water retention relation is important in quantifying soil moisture dynamics, as discussed later. Another area in which it is important is in soilplantwater relations. Often termed matric potential because it is representative of the energy state of the soil water, c indicates the work that must be done by plant roots to extract water from the unsaturated soil. Plants wilt from inadequate soil moisture not in direct response to low y, but rather because at low y, c is low. In soil that is too dry, c is so highly negative that a plant is incapable of over- coming this energy barrier. Typically, the minimum c is about 15 atm for agricultural plants, though much lower in some plants, especially those native to arid regions. Measurement or estimation of water retention Any system that makes independent simultaneous mea- surements of y and c can indicate the water retention relation. In addition, there are methods specifically intended to measure this property. Many of these methods use a porous membrane, often ceramic, to permit equilibration of water pressure between the porous medium on one side of the membrane with bulk water on the other, as in tensiometers (Figure 4). The pressure of this bulk water (and hence the pore- water pressure) is controlled, as is the air pressure in the medium, in order to control c. The pressure, or less commonly the volume of water, is adjusted through a planned sequence, and paired values of c and y (one of them controlled and the other measured) represent the retention curve. Because various nonhydraulic properties of a medium, especially particle-size distribution, correlate in some way with water retention but are considerably easier to measure, property-transfer models have been developed for estimating water retention from other properties. One broad class of such models is based on theoretical relationships between pore sizes and particle sizes. Models of this type may work reasonably well for sandy media. Another class of such models uses statistically calibrated pedotransfer functions. The basis for this type of model is not a principle like the correlation of pore and particle size, but rather a data- base of measured water retention and other properties for a wide variety of media. Given a mediums particle- size distribution and other properties such as organic matter content, a pedotransfer function can estimate a retention curve with good statistical comparability to retention curves of other media in the database whose nonhydraulic properties may be similar. Whatever the choice of model, however, without any retention mea- surements for the medium in question, it is usually impossible to know whether the model result is a good representation of the retention curve. Empirical formulas for water retention In general, a water retention curve can be represented by measured data, interpolated as needed. It is often convenient, however, to express the curve as a parametric empiri- cal formula. Among the most widely used empirical formulas are that of Brooks and Corey max min b b min 1 where cb, b, and ymin are fitted empirical parameters and ymax is the maximum value of y, and that of van Genuchten max min 1 1 c 2 6 4 3 7 5 min 2 where cc, n, m, and ymin are fitted empirical para- meters. Fundamentally, ymin should equal zero, but a finite value is often used to improve the fit in the higher-y portion of the curve. Equations as simplified as these cannot represent the precise form of the yc relation of a natural medium, though they may serve for various practical purposes. Diffuse Unsaturated Flow Traditionally, unsaturated flow is considered as a continuum in which the average behavior of water in many pores within a compact region of space (a representative elementary volume (REV)) represents the characteristics of the medium point-by-point. In general, this leads to a conceptualization of mois- ture varying systematically throughout the medium (Figure 6). In conventional unsaturated flow theory, two types of factors determine water flux: driving forces (chiefly gravity and matric pressure gradients) and properties of the medium. The matric forces sometimes greatly Hydrology _ Vadose Water 79 exceed the gravitational force. Other forces may also drive flow under some conditions, as when tempera- ture or osmotic gradients are significant. Darcys law for vadose water Unsaturated flow has its basic mathematical expression in Darcys law, in a form such as q K g d dz g 3 where q is the flux density, K is the unsaturated hydraulic conductivity, r is the density of water, g is the acceleration of gravity, and z is upward distance. The conversion factor 1/rg is shown here explicitly so that this expression can be used directly with c in SI pressure units (kPa), and K in velocity units (m/s). In head units, c takes dimensions of length. Unsteady diffuse flow In the general case of tran- sient (nonsteady) unsaturated flow, the flow itself causes y to change throughout the medium, which leads to continuously changing hydraulic conductiv- ity and driving forces. These interacting processes can be accommodated mathematically by combining the equation of continuity @ @t @q @z 4 with Darcys law [3] to get Richards equation, which for one-dimensional vertical flow within a medium in earth gravity can be written as C @ @t 1 g @ @z K @ @z @K @z 5 where C is the differential water capacity, a property of the medium defined as dy/dc. It is also possible to formulate this equation in terms of y rather than c. In general the equation can be solved numerically. Unsaturated hydraulic conductivity K of the me- dium depends on the whole set of filled pores, espe- cially on their size, shape, and connectedness. In unsaturated media, as illustrated by the measure- ments in Figure 7, K depends very strongly on y. Because the large pores empty first as y decreases, the result is not only that fewer pores are filled to conduct water, but the remaining filled pores are smaller and therefore less conductive. With fewer pores filled, the paths of water flowing though the medium also become more tortuous. When the soil is quite dry, very few pores are filled, and the water moves mainly through poorly conducting films adher- ing to particle surfaces. The net effect of these factors is to reduce hydraulic conductivity by several orders of magnitude as the soil goes from saturation to typi- cal field-dry conditions. Measurement or estimation of unsaturated K The most accurate measurements of hydraulic conductiv- ity are by steady-state methods. One technique is to establish constant (though not necessarily equal) pressures of water at two opposing faces of a porous medium, measure the flux density, and calculate K using Darcys law. Another is to force water through the medium at a constant and known flux density, which lets c become uniform in part of the sample, then to compute K from the known flux density and force of gravity. With gravity as the main driving force, steady-state measurements are possible only for the high K values of fairly wet soil. Centrifugal Steady state, centrifuge Water content (vol/vol) Transient, inversion method Steady state, gravity Oakley sand Hydraulicconductivity(m/s) 0 1011 109 107 105 0.10 0.2 0.3 0.4 Figure 7 Hydraulic conductivity for a sandy soil (Oakley sand), measured by three methods. Diffuse flow in soil Meters 0 1 2 3 4 Figure 6 A diffuse distribution of water in soil. Blue shading indicates wetter soil over most of the upper half of this profile, especially to the right. Drier soil is lower and to the left. The transition between wet and dry soil is gradual and spread over a considerable volume. 80 Hydrology _ Vadose Water force makes possible the accurate measurement of K at low y. Many techniques for measuring unsaturated hydraulic conductivity use unsteady flow. One of these is the instantaneous-profile method, useful in both laboratory and field. This method uses measure- ments of y and c within a medium in which unsteady flow has been established, so that both the flux density and the c gradient can be computed at one or more instants of time. Another alternative for laboratory applications uses flow driven by evaporation. There are various indirect and inverse methods a wide variety of situations where data are available describ- ing water flow over time can provide information for an estimation of K. The tension infiltrometer method is in widespread use for field applications. This method uses the measured infiltration rate as a function of time for water applied at controlled c values to calculate the unsaturated hydraulic prop- erties. It is often implemented as an inverse method. Property-transfer models can be useful for estimat- ing K. Usually these use water retention, not particle- size distribution, as the more easily measured type of data from which unsaturated K is calculated. If a transfer from particle size to K is needed, such a model may be combined with a water retention pro- perty-transfer model, though reliability is likely to be reduced because the particle-size distribution is less directly related to K. Capillary theory provides an interpretation of the pores in the medium that relates to both retention and K. Models developed by Mualem and Burdine have become widely used for this purpose. A direct combi- nation of an empirical formula for water retention, such as [1] or [2], into a capillary-theory formulation of unsaturated K can yield a convenient analytical formula for K(y), and facilitate the combined treat- ment of water retention and unsaturated K. Empirical formulas for unsaturated K As in the case of water retention, completely empirical formulas can represent unsaturated K. Gardner, for example, used K A exp 6 where A and a are fitted empirical parameters. Such formulas have greater simplicity and sometimes lead to more realistic curve shapes than formulas devel- oped for combined representation of K and water retention. The a parameter in [6] is used in developing and applying other models, such as analytical solu- tions of equations representing unsaturated flow. Effects of dissimilar materials Layers that contrast in hydraulic properties impede vertical flow by various mechanisms. When water moves down from a coarse to a fine layer, as from coarse sand to silt, if both layers are near saturation, the fine layer has smaller hydraulic conductivity; therefore, flow slows when it reaches the fine layer. If, however, the coarse layer is nearly saturated but the fine layer is initially fairly dry, at first the flow may be temporarily accel- erated while the flow is dominated by the sorptive nature of the fine medium, which tends to suck water out of the coarse material. When water moves down from a fine to a coarse layer it will also be impeded under many circumstances. Dry coarse material has an extremely small hydraulic conductivity; thus it tends not to admit water into the pores and exhibits a somewhat self-perpetuating resistance to flow. Water breaks into the coarse layer if the pressure at the layer contact builds to the point that the water- entry pressure (the minimum water pressure needed to fill an empty pore) of some of the large pores is exceeded. This can generate flow instabilities. Stable or not, water flow into the pores of the coarse medium increases that mediums hydraulic conduc- tivity. With equal c values across the layer boundary, unsaturated K of the coarse layer is often less than that of the fine layer. In general, stable or diffuse flow through layers where fine overlies coarse is slower than it would be if both layers had the properties of the fine medium. Preferential Flow In recent decades it has become increasingly clear that much unsaturated-zone transport of importance, especially when water is abundant, occurs through a small fraction of the medium along preferential paths such as wormholes, fractures, fingers of enhanced wetness, and regions near contacts between dissimilar portions of the medium. This flow, for which accepted theory applies less well, occurs at rates typically some orders of magnitude faster than flow through the remainder of the medium. In many applications, its importance is redoubled because preferentially trans- ported substances are exposed to only a small fraction of the soil or rock and only for limited time, reducing opportunity for adsorption or reactions. Types of preferential flow Three basic modes of preferential flow (Figure 8) are (1) macropore flow, through pores distinguished from other pores by their larger size, greater continuity, or other attributes that can enhance flow; (2) funneled (or deflected or focused) flow, caused by flow-impeding features of the medium that concentrate flow in adjacent zones that are highly wetted and conductive; and (3) unstable flow, which concentrates flow in wet, conductive fingers. Hydrology _ Vadose Water 81 Common macropores include wormholes, root holes, and fractures (Figure 9). When macropores are filled with water, flow through them is fast. When they are empty, there may be essentially no flow through the macropores themselves though in some conditions film flow along macropore walls is significant. Macropores that are partly filled with water provide a variety of possibilities for the configuration and flow behavior of water. Funneled flow commonly occurs with contrast- ing layers or lenses, where flow deflected in direc- tion becomes spatially concentrated (Figure 10). The local increase in y causes a corresponding increase in hydraulic conductivity and flux, and usually a change in the predominant direction of flow. Unstable variations in flow and water content, even within a uniform portion of the medium, can increase flow rates considerably. A typical case has a layer of fine material above the coarse material. Downward- percolating water builds up significantly at the inter- face, and breaks through into the coarse medium at a few points. The material near individual points of breakthrough becomes wetter and hence much more conductive. For some time thereafter, additional flow into the coarse material moves in the few fingers that are already wet (Figure 11). Between fingers, the medium can be relatively dry. In addition to textural contrasts, hydrophobicity (water repellency) and air trapping may cause flow instability. Quantification of preferential flow One straightfor- ward quantitative treatment is to represent preferen- tial flowpaths with discrete conduits whose geometry, with appropriate laminar-flow expressions, predict the flow rate through the part of the medium they occupy. Usually this requires a statistical characteri- zation of the set of conducting pathways, because the position, number, shape, orientation, and connected- ness of the individual pathways are unknown. Perhaps more widely used are various forms of equivalent-medium approach. The key assumption is that the effective hydraulic properties of a large volume of the medium that includes preferential path- ways are equivalent to the average properties of a Planar structure Root Pond 1 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 1.0 QAa9854c Width (m) Depth(m) Distribution zone Soil surface Figure 9 Macropore flow paths highlighted using a dye tracer. Reproduced from Scanlon BR and Goldsmith RS (1997) Field study of spatial variability in unsaturated flow beneath and adjacent to playas. Water Resources Research 33: 22392252, with permission from the American Geophysical Union (http:// Coarse sand layers Red dye plumes Plow zone 1.5m Furrows where red dye was applied Potato hills Figure 10 Funneled flow identified using a dye tracer. Reproduced from Kung KJS (1990) Preferential flow in a sandy vadose zone: 1. Field observation. Geoderma 46: 5158, with permission from Elsevier. Meters Soil Macropores Sand or clay lenses 0 1 2 3 4 Figure 8 Three basic types of preferential flow. Arrows indicate narrow regions of faster flow than their surroundings. Macropore flow occurs through channels created by aggregation, biotic activity, or similar causes. Funneled flow occurs when flow is deflected by heterogeneities of the medium so as to create zones of higher water content and greater K. Unstable flow can be generated at layer boundaries such as the bottom of a sand lens at right, where flow into the lower layer moves in the form of highly wetted fingers separated by regions of relatively dry soil. 82 Hydrology _ Vadose Water hypothetical homogeneous granular porous medium. The effective hydraulic properties then can be applied directly in numerical simulators using Darcys law and Richards equation. A major advantage of such an approach is that the many existing theories, models, and techniques developed for diffuse flow in granular media can be applied to preferential flow. A major drawback is that preferential flow may devi- ate significantly from behavior describable using this type of medium, precluding reliable results. It is also a common practice to treat preferential flow differently from nonpreferential flow (often com- bined with a conventional Richards equation for the matrix flow). Vadose Water in the Hydrologic Cycle Moisture State in the Vadose Zone The water content and matric pressure within the vadose zone influence and in turn are influenced by conditions in the saturated zone and atmosphere. The distribution of vadose water at a given time also depends on the energy state (whose components include matric and gravitational potential), wetting/ drying history, and dynamics of the water itself. If there is no flow, one can infer that the gradient of total potential is zero, so if the matric and gravita- tional components are the only significant ones, they add to a constant total potential. Figure 12(a) shows this type of hydrostatic profile for the case where a water table is present. Since the matric pressure in this case is linear with depth and y is controlled by the water retention properties of the medium, for a uniform vadose zone, the y profile (not shown here) mimics the shape of the water retention curve. Given time, approximate versions of such a hydro- static profile may develop in portions of a profile where water movement is negligible. If water flows 52.5 cm 98cm 150 50 250 350 450 550 Figure 11 Fingers generated in unstable flow in a laboratory investigation, showing the extent of wetted soil as a sequence in time. Numerals on the diagram indicate the number of seconds since flow began. Reproduced from Selker J, Leclerq P, Parlange JY, and Steenhuis T (1992) Fingered flow in two dimensions 1. Measurement of matric potential. Water Resources Research 28: 25132521, with permission from the American Geophysical Union ( copyright.html). Z (cm) 800 400 (a) 800 400 Total GravitationalMatric (b) 800 (c) 800 400 0 400 400 800 Potential (cm-water) Figure 12 Profiles of matric, gravitational, and total potential for idealized situations of (a) static water, (b) steady downward flow, and (c) unsteady flow. The water table is at z 0. Hydrology _ Vadose Water 83 vertically downward at a steady rate in a homoge- neous medium, the total gradient must be constant, but the matric pressure does not cancel out the gravi- tational potential, as illustrated in Figure 12(b). In the general case of unsteady flow, the matric pressure profile cannot be determined so simply, and may take on an irregular form as in Figure 12(c). The uppermost part of the water distribution pro- file is sometimes described in relation to field capac- ity, defined as the water content of a soil profile when the rate of downward flow has become negligible 2 or 3 days after a major infiltration. This concept is used in agriculture to indicate the wettest soil conditions to be considered for plant growth, and sometimes is mentioned in hydrologic investigations related to soil moisture storage. The definition of field capacity requires some subjective judgment, for example, in deciding what flow is negligible. Field capacity is implicitly associated with the entire soil profile through the root zone, including preferential-flow characteris- tics and, especially, flow-retarding layers that enable layers above them to retain a high water content. In a portion of the vadose zone immediately above the water table, it may happen that all pores are filled with water, held by capillary forces. The depth inter- val that is saturated but above the water table is called a capillary fringe. In a hydrostatic profile, this cor- responds to a flat portion of the retention curve between saturation and an air-entry pressure. Some media do not have a significant capillary fringe be- cause their retention characteristics have the air-entry pressure at essentially zero. Where the water table fluctuates, the hydrostatic equilibrium needed for a capillary fringe may take considerable time to estab- lish. Soilwater hysteresis would make for a different capillary fringe with a falling water table than with a rising water table. Moisture Dynamics in the Vadose Zone Interactions at the land surface Infiltration Infiltration is the downward movement of water through the land surface. If the soil is initi- ally dry, c gradients may be the predominant down- ward driving force. When the soil is very wet to some depth, gravity may dominate instead. The usual case is that water infiltrates faster at the start and slows down as a zone of increased water content develops at the surface and expands. Figure 13 shows actual infiltration rates varying over time in three soils. Mathematically, the decline of infiltration rate as the soil gets wetter is frequently represented by an inverse proportionality to the square root of time, as predicted by several models of infiltration. If water at the surface is abundantly available, but not under significant pressure, infiltration occurs at the infiltra- tion capacity, a rate determined by the soil rather than the rate of application or other factors. If water arrives at the land surface faster than the infiltration capacity, excess water ponds or runs off. Like hydrau- lic conductivity, infiltration capacity is not single- valued for a given medium but varies with water content and other conditions. Conditions that com- plicate the ideal conception of infiltration include: variation of application rate with time, spatial varia- bility of soil and surface properties, water repellency of the soil, air trapping, and variations of temperature. Evapotranspiration The transport of water from soil through plants to the atmosphere (known as 0 20 15 10 5 0 High infiltration-rate soil Infiltrationrate,cmhr1 Moderate infiltration-rate soil Low infiltration-rate soil Time-hours 5 10 15 20 25 30 Figure 13 Measured infiltration rates over time for three different soils. Reproduced from Swarner LR (1959) Irrigation on western farms. Agriculture Information Bulletin 199, U.S. Department of Interior and U.S. Department of Agriculture: Washington, DC. 84 Hydrology _ Vadose Water transpiration) and the direct transport from soil to atmosphere (known as evaporation) together con- stitute evapotranspiration. When the soil is wet enough, atmospheric conditions control the evapora- tion rate. When the soil is too dry to supply water at the maximum rate the atmosphere can absorb, the soil properties will control the evaporation rate. Thus there are at least two cases to consider: the atmosphere-dominated constant-rate phase during which the transport mechanisms of the soil are ignored, and the soil-dominated declining-rate phase, during which atmospheric effects are ignored. On vegetated land, transpiration typically far exceeds evaporation. Capillary forces can draw water up from the water table to depths from which it supplies the process of evapotranspiration, which can be a substantial loss mechanism from a water-table aqui- fer, especially where the vadose zone is thin. Redistribution of infiltrated water After water has infiltrated, it redistributes, driven by gravity, matric pressure gradients, and possibly other forces. Figure 14 illustrates y distributions at various times during and after infiltration, in a mechanically 0 0 100 200 300 400 500 Undisturbed hole 3 Disturbed hole 19 Disturbed hole 19 Undisturbed hole 3 600 (a) (c) (d) (b) 100 Depth(cm) 200 Initial 76 d 32 d 10 d 2 d 24 hr 6 hr 12 hr 18 hr 24 hr 300 400 500 600 0.1 0.2 0.3 0.4 0.1 Water content (vol/vol) 0.2 0.3 0.4 Figure 14 Measured water distributions during and after 24 h of flood infiltration in (a, b) an undisturbed soil on the Snake River Plain in Idaho and (c, d) nearby soil that was disturbed by temporary removal and replacement. Evaporation was inhibited by an impermeable cover at the land surface. Reproduced from Nimmo JR, Shakofsky SM, Kaminsky JF, and Lords GS (1999) Laboratory and field hydrologic characterization of the shallow subsurface at an Idaho National Engineering and Environmental Laboratory waste-disposal site. Water-Resources Investigations Report 994263, U.S. Geological Survey: Idaho Falls, Idaho. Hydrology _ Vadose Water 85 disturbed soil and in a soil with intact natural struc- ture. Redistribution continues until all forces balance out. Equivalently, the water may be considered to progress toward a state of minimal (and uniform) total energy of the earthwaterair system, i.e., equilibrium. Normally hysteresis strongly influences redistribu- tion because a wetting front progresses downward according to the wetting curves of water retention and conductivity, whereas y in the upper portions of the wetted zone decreases according to the drying curves. Because a drying retention curve has greater y for a given c, water contents remain higher in the upper portions than they would if there were no hysteresis. Thus one important consequence of hys- teresis is to hold more water near the land surface where it is accessible to plants. Usually, the above considerations need to be ad- justed or reinterpreted with attention to preferential flow. Qualitatively, a major effect of preferential flow is to permit more rapid movement of water to signifi- cant depths. This would occur primarily under very wet conditions, and would be followed in the redistri- bution process by a slower flow of water into the regions between preferential flow channels. A common phenomenon in layered media is perch- ing, the accumulation of water in a region of the vadose zone to the point where it becomes saturated even though there is unsaturated material between that region and the water table. The high water con- tent of a perched zone causes greater hydraulic conductivity and potentially faster transport through the three-dimensional system. The main effect is not a direct increase in vertical flow, though possibly in horizontal flow. New and different conditions may affect biological and chemical processes in a perched zone, e.g., reduced aeration. A situation comparable to perching exists when a body of surface water has a vadose zone underneath it (Figure 15). This may be caused by a flow-restricting layer at or beneath a lakebed or streambed. The situa- tion may alternatively be thought of as a perched water body directly under the lake or stream. The key condition is that the impeding layer must reduce the downward flow rate to less than the saturated hydraulic conductivity of the layer immediately below it. Another way this can happen is as a transient response to ephemeral surface water, below which an unsaturated state may persist for some time after standing water has come into the depression or channel. Aquifer Recharge Aquifer recharge is water that moves from the land surface or unsaturated zone into the saturated zone. Quantitative estimation of recharge rate contributes to the understanding of large-scale hydrologic pro- cesses. It is important for evaluating the sustain- ability of groundwater supplies, though it does not equate with a sustainable rate of extraction. Where contamination of an aquifer is a concern, estimating the recharge rate is a first step toward predicting solute transport to the aquifer. Recharge may cause a short- or long-term rise of the water table. Artificial drainage, e.g., with horizontal porous pipes buried at a chosen depth, is sometimes used to maintain a minimal thick- ness of vadose zone for agricultural or other purposes. Recharge rates vary considerably in time and space. Recharge often occurs episodically in response to storms and other short-term, high-intensity inputs. For a given amount of infiltration, temporal concen- tration enhances recharge because it entails shorter residence times for water in the portions of the soil from which evapotranspiration takes place. Similarly, a larger fraction will become recharge if it is concen- trated in narrow channels such as fingers or macro- pores, not only because this tends to hasten its passage through the unsaturated zone, but also because the water then occupies less of the volume of soil from which evapotranspiration takes place. Conclusion The state and dynamics of vadose water are compli- cated by the interaction of multiple phases. At least three drastically different substances water, air, and solid mineral are critical to its nature and quantifi- cation. Unsaturated flow phenomena are extremely sensitive to the proportions of those phases, especially the fluid phases, as natural variations in the relative amounts of water and air can cause a property like hydraulic conductivity to vary over many orders of magnitude. When the flow of vadose water is diffuse in character, it can be treated quantitatively Unsaturated zone Water table Figure 15 A stream, disconnected from the water table, so that interaction between surface water and the aquifer occurs through the unsaturated zone. Adapted from Winter TC, Harvey JW, Franke LO, and Alley WM (1998) Ground water and surface water A single resource. Circular 1139, U.S. Geological Survey. 86 Hydrology _ Vadose Water with Darcys law adapted for unsaturated flow, and with Richards equation. When it occurs within pref- erential pathways, there are various models, none yet generally accepted, to quantify the flow. The state and dynamics of vadose water control or contribute to a wide variety of processes within the hydrologic cycle, including infiltration, evapotranspiration, infiltration and runoff, and aquifer recharge. See also: Atmospheric Water and Precipitation; Evapotranspiration; Ground Water; Hydrological Cycle and Water Budgets. Further Reading Bear J and Bachmat Y (1990) Introduction to Modeling Phenomena of Transport in Porous Media. Dordrecht, Netherlands: Kluwer. Dane JH and Topp GC (2002) Methods of Soil Analysis, Part 4 Physical Methods. Madison, WI: Soil Science Society of America. Gardner WH (1986) Early soil physics into the mid-20th century. In: Stewart BA (ed.) Advances in Soil Science, vol. 4, pp. 1101. New York: Springer-Verlag. Germann PF and DiPietro L (1996) When is porous-media flow preferential? A hydromechanical perspective. Geoderma 74: 121. Hillel D (1998) Environmental Soil Physics. San Diego: Academic Press. Simunek J, Jarvis NJ, van Genuchten MT, and Gardenas A (2003) Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone. Journal of Hydrology 272: 1435. Jury WA and Horton R (2004) Soil Physics. New York: Wiley. Nimmo JR (2005) Unsaturated zone flow processes. In: Anderson MG and Bear J (eds.) Encyclopedia of Hydrological Sciences, vol. 4, pp. 22992322. Chichester, UK: Wiley. Nimmo JR (2007) Simple predictions of maximum transport rate in unsaturated soil and rock. Water Resources Research 43: W05426, doi:10.1029/2006WR005372. Scanlon BR, Tyler SW, and Wierenga PJ (1997) Hydrologic issues in arid unsaturated systems and implications for contaminant transport. Reviews of Geophysics 35: 461490. Hydrology _ Vadose Water 87 Ground Water W M Alley, U.S. Geological Survey, San Diego, CA, USA Published by Elsevier Inc. Introduction Ground water occurs almost everywhere beneath the land surface and is an integral part of a complex hydrologic cycle that involves continuous movement of water on Earth. The widespread occurrence of potable ground water is a major reason for its use as a source of water supply worldwide. Furthermore, much of the worlds food is produced by irrigated agriculture, which relies on ground water. Ground water plays a crucial role in sustaining streamflow during dry periods and is vital to many lakes and wetlands. In addition to human uses, many plants and aquatic animals depend upon the ground water that discharges to streams, lakes, and wetlands. Ground water is a hidden resource. Information is gained at individual wells and spring locations, through indirect methods of measurement such as surface geophysics, and by measurements of flow and water level at hydrologically connected water bodies such as streams, lakes, and wetlands. These data are used to infer the occurrence, movement, and properties of ground water. Aquifer Basics Water-level measurement in a tightly cased well is a measurement of the hydraulic head (often simply referred to as head) in the aquifer at the depth of the screened or open interval of a well. Because the head represents the energy of water, ground water flows from locations of higher head to lower head. For simplicity, we use the terms water level and head interchangeably in this article. Two general types of aquifers unconfined and confined are recognized (Figure 1). In unconfined aquifers, heads fluctuate freely in response to changes in recharge and discharge. Water levels measured in wells completed in the upper part of an unconfined aquifer help define the elevation of the water table, which is the top of the saturated zone. In confined aquifers, sometimes known as artesian aquifers, water in the aquifer is confined under pressure by a geological body that is much less permeable than the aquifer itself. Many aquifers are intermediate between unconfined and confined conditions. The removal of water by pumping sets up hydraulic gradients that induce flow from the aquifer to the well. The principal mechanism of aquifer drainage in response to pumping depends on whether an aqui- fer is unconfined or confined. Water drawn from stor- age in an unconfined aquifer comes from dewatering of the aquifer material by gravity drainage. Confined aquifers, which are filled by water under pressure, respond to pumping differently. The water for pump- ing is derived not from pore drainage but from aquifer compression and water expansion as the hydraulic pressure is reduced. Pumping from confined aquifers typically results in more rapid water-level declines covering much larger areas when compared with pumping the same quantity of water from unconfined aquifers. Drawdowns in water levels (heads) in the confined aquifer will induce leakage from adjacent confining units. Slow leakage over large areas can result in the confining unit supplying much, if not most, of the water derived from pumping. In some hydrogeologic terrains, the removal of water can cause compaction of fine-grained beds with resultant subsidence of the land surface. If water levels are reduced to the point where an aquifer changes from a confined to an unconfined condition (becomes dewatered), the source of water becomes gravity drainage as in an unconfined aquifer. The equation that describes the movement of ground water within a porous medium is known as Darcys law: Q KAi; where Q is the rate of flow or volume per unit of time [L3 T1 ], K is the hydraulic conductivity [LT1 ], A is the cross-sectional area [L2 ], and i is the hydraulic gradient (the change in head per unit of distance; dimensionless), which is a negative number in the direction of flow. The average linear velocity of the water can be calculated from Darcys law by dividing by the cross-sectional area and effective porosity of the rock through which the water moves: v Ki=n; where v is the average linear velocity (referred to as velocity for the remainder of the text) of the ground water [LT1 ] and n is the effective porosity (dimensionless). The hydraulic conductivity, hydraulic gradient, and effective porosity are all important in determining the movement of ground water. The hydraulic conductiv- ity, which represents the ability of the geologic frame- work to transmit water, is a property of the porous 88 medium and the fluid contained therein. The hydrau- lic conductivity of a groundwater system can vary over many orders of magnitude. The larger the hydraulic conductivity of a porous medium, the easier it is for water to flow through it. The porosity is the ratio of the volume of the voids divided by the total volume. The effective porosity is the volume of the voids that are interconnected and available for fluid transmission divided by the total volume. For ground water flow in cavernous karst terrain or in fractured- rock systems, the validity of Darcys law, which was developed for porous media, may not be strictly applicable, and other methods for determining the velocity distribution may be required. Groundwater Flow Systems The three-dimensional body of Earth material saturated with moving ground water that extends from areas of recharge to areas of discharge (Figure 1) is referred to as a groundwater flow system (or more simply as a groundwater system). The areal extent of groundwater systems varies from a few square kilometers or less to tens of thousands of square kilometers. The lengths of groundwater flow paths range from a few meters to tens, and sometimes hundreds, of kilometers. A deep groundwater system with long flow paths between areas of recharge and discharge may be overlain by, and in hydraulic connec- tion with, several shallow, more local, flow systems. The age (time since recharge) of ground water var- ies in different parts of groundwater systems. The age of ground water increases along a particular flow path through the groundwater system from an area of recharge to an area of discharge. Travel times within groundwater systems can vary considerably (Figure 1). In shallow flow systems, ages of ground water at areas of discharge can vary from less than a day to a few hundred years. In deep, regional flow systems with long flow paths (tens of kilometers), ages of ground water may reach thousands or tens of thousands of years or more. Fractured-rock systems in bedrock usually have smaller effective porosities than unconsolidated porous media such as sands and gravels, and flow velocities through fractured rock can be relatively fast. In more sluggish groundwater systems, long- term climate and geologic change need to be consid- ered in understanding the movement of ground water over tens of thousands of years. Tracer techniques have been applied widely to estimate the residence time of subsurface waters, as well as the amounts and timing of recharge and dis- charge. Most tracer techniques require knowledge (or assumption) of the time history of tracer input at the land surface or the water table. This temporal pattern is then correlated to a concentrationdepth pattern in the subsurface at a point in time. Other approaches use information on decay products to determine age. Tracers can occur naturally (chloride, heat, the stable isotopes of hydrogen and oxygen in the water Pumped well Recharge area Stream Discharge area Days Years Years D ays Centuries Millennia Confining bed Confining bed Confined aquifer Unconfined aquifer Confined aquifer Water table Figure 1 Ground water system showing generalized flow paths of groundwater movement and the relative age of the water since the time of recharge. Adapted from Heath RC (1983) Basic ground-water hydrology. U.S. Geological Survey Water-Supply Paper 2220. Hydrology _ Ground Water 89 molecule), occur in the atmosphere as a result of human activities (tritium, CFCs), or be applied inten- tionally on the land surface (fertilizers, pesticides). Isotopes of elements, such as radon, dissolved from host rocks can also be used to estimate residence times and interactions with surface water. Over the past decade, research in age dating and tracking young ground water ( volcanic ash > loose sedimentary rocks > shales > sandstone > hard volcanic rocks > other crystalline rocks). Nonweathered rocks (e.g., those exposed after glacial erosion) are also less erodible than those exposed to weathering over long periods.YTSS also decreases with catchment size as the opportunity for redeposition in floodplain increases.YTSS is naturally very low at lake outlets, e.g., Saint Lawrence and Neva rivers (Table 1), because of particulate settling. The sediment fluxes of rivers have greatly changed over time in response to human impact. On the one hand, sediment loads are increasing because of land clearance for agriculture and other land surface distur- bance. Forest clear-cutting on steep slopes is responsi- ble for the most abrupt changes, as observed in Papua New Guinea in the last 100 years. In other regions, the sediment increase started in earlier, some 2000 years ago (Danube) and 1000 years ago (Ebro River in Spain) (Walling, 2006). On the other hand, the trap- ping of sediments at the global scale by hundreds and thousands of small reservoirs (volume V < 103 km3 ) and a few dozen of very large ones (V > 10km3 ) is now widespread and has already had an impact at the global scale: more than 30% of river sediments gener- ated by mechanical erosion is intercepted and stored by reservoirs. The global range of median TSS concentrations in rivers (C50), of discharge-weighted concentrations (C*), and of their related daily sediment yields (Y50 and Y*) are presented in Table 1 together with the percentage of time necessary to carry half of the sediment flux (Ts50%). The geographic variability is enormous, due to the hydrological regimes, relief, or basin size. It is also important to note the difference between median values (C50,Y50) generally obtained from classical water quality surveys and discharge- weighted values (C*,Y*) based on daily surveys, par- ticularly during floods. The spatial distribution of interannual TSS concen- trations and fluxes indicators is presented on Table 1 for a set of rivers (exceeding 1000 km2 ) that represent a wide variety of river regimes. All indicators vary over several orders of magnitudes, depending on local or regional conditions. Flux[%] Sediment 99.8 99.5 99 98 95 9090 99 80 70 60 50 50 40 30 20 10 5 1 5 Time [%] KLM Time [%] Water 0.5 1 2 5 10 25 500.5 1 2 5 10 25 50 NMS MAT RHL Figure 1 Flux duration curves for water and suspended particulate matter: percent of fluxes discharged in percent of time (Henry Law probability scale). Examples for the Khong Mala (KLM,Thailand) the Nam mae Pai (NMS, Thailand) the Matanuska (MAT, Alaska) and the Rhone Lacustre (RHL,Switzerland). Adapted from Meybeck M, Laroche L, Du rr HH, and Syvitski JPM (2003) Global variability of daily total suspended solids and their fluxes in rivers.Global Planetary Change 39: 6593. Hydrology _ Fluvial Export 121 Table 1 Global range of concentrations and fluxes of suspended particulate matter (SPM) in rivers surveyed at the daily scale, medium and large basins Very low Low Medium High Very high Extremely high Cs* (mg l1 ) Discharge-weighted total suspended solids 520 20100 100500 5002000 200010 000 >10 000 Bandama Arve Eel Pecos Annapolis Chaudie` re Huai Mae Ya Matanuska Piray Colorado Rhone Lacustre Loire Red Deer Mekong Rio Grande El Abid St. Lawrence Sacramento Stikine Mississippi Walla-Walla Little Colorado Y * (kg km2 day1 ) Average daily suspended solids yields 5000 Annapolis Khlong Mala Colorado Gambia Nzi Chaudie` re Mississippi Eel Alpine Rhine Rhone Lacustre St. Lawrence Middle Rhine Peace El Abid Espejos Somme Sacramento Pecos Matanuska Salween Cs*/ Cs50 Weighted-suspended solids variability 12 25 510 1020 2050 >50 Loire Annapolis Mississippi Bani Arve Alpine Rhine Peace Eel Rio Grande Fraser Chaudie` re Matanuska Red Deer Walla-Walla Seine Lot Salween Stikine Y */ Y50 Suspended solids flux variability 50 Mississippi Bandama Bani Gambia Alpine Rhine Eel Rhone Lacustre El Abid Colorado Khlong Sok Peace Matanuska Somme Fyris Fraser Peace Piray Red Deer St. Lawrence Rio Grande Rhone Alpestre South Saskat. Stikine Walla-Walla Ts50% Percentage of time needed to carry half of the sediment flux >16.5% 16.58% 83.4% 3.41.4% 1.40.4% 5 meq l1 ) in which SO4 2 and Cl are gradually dominant. Pyritic shales provide waters with high natural SO2 4 levels. Examples of lithology influence on river ionic composition can be found in Hem (1989) and Meybeck (2003). Silica originates from the weathering of silica minerals found in crystalline rocks particularly in volcanic rocks (olivine), and of amorphous silica found in some sedimentary rocks (chalk). High silica levels are thus found in volcanic catchments (Table 4) (Tone and Shinano rivers, Japan, see Table 4), in chalky catchments rich in amorphous silica (Thames), and downstream of hydrothermal fields (Waikato River, New Zealand). The lowest silica levels are noted in lake-dominated catchments (Churchill, Neva, St Lawrence rivers) because of the SiO2 uptake by diatoms. Similar silica uptake is often noted down- stream of reservoirs cascades in impounded catch- ments. There is a growing evidence of silica control by the terrestrial vegetation and soil phytoliths. At global scale, annual average yields of major ions and silica increase with the river runoff; second-order variations result from the catchment lithology. In rivers draining arid and semiarid regions (q < 30 mm year1 ), the evaporation leads to a progressive pre- cipitation of salts and yields are very limited, as in Central Asia. Major World Rivers and Their Ranked Fluxes River flows and catchment areas are now well docu- mented on most major rivers (Table 2). The Amazon and Congo rivers are respectively # 1 and 2 with regards to annual flow (Q in km3 year1 ; 1 km3 year1 is equivalent to an average discharge of 31.7 m3 s1 ), followed by the Orinoco, Chang Jiang (Yang Tse), Yenisey, and Parana. Figures listed in Tables 2 and 3 include both rivers in pristine state and those already impacted by pollution, damming, irrigation, and diversion. Such dataset has some degree of uncertainty, also it is continuously revised: (i) recent studies on the Amazon have lead to modi- fications for both Q and FTSS; (ii) some natural fluxes estimates are relatively old, although they cannot be checked today due to their present land use change; (iii) damming and irrigation are progressing in many regions of the world and therefore average Q and Ms are not stable; even in large river basins, erosion control measures can also be efficient and reduce sediment yields, as for the Yellow River (Huang He); (iv) river TDS may be greatly affected by pollution; (v) river drainage area in dry regions is difficult to be defined as large portions only contribute occa- sionally (e.g., Nile, Niger). The rivers for which present sediment load is certainly much lower than natural figures are indicated by an asterisk. The concept of the worlds greatest rivers is not applicable; top-ranked rivers are very different for each river attribute: catchment area, length, flow, fluxes of dissolved salts, and particulate matter. Rivers drained to the oceans (exorheic, Tables 2 and 3) are only considered here. Some rivers correspond to internal drainage (endorheic) as Volga (Russia), Chari (Central Africa), 124 Hydrology _ Fluvial Export Table 3 Miscellaneous river fluxes to oceans: water discharge (Q), annual runoff (q), suspended sediment fluxes (FTSS), dissolved fluxes (FTDS) and river length (L) River River flow Basin area Sediment flux Dissolved flux River length Qnat (km3 /y) # qnat (mm/y) Qp (km3 /y) A (Mkm2 ) # Ms (Mt/y) # Msp (Mt/y) Md (Mt/y) # L (km) # Churchill (Hudson Bay) 40 87 25.8 0.298 48 3.45 1600 Colorado (US/Mexico) 18.5 29 0.1 0.639 30 120 16 ***0.1 [20.5] [26] 2330 30 Copper 56.6 831 0.063 70 24 460 Dnepr 106 53 0.5 34 2.3 *** 14.6 2200 Don 49 20.7 0.42 38 4.8 *** 17.1 37 1870 Elbe 23.7 162 0.146 70 0.84 (17.2) (36) 1110 Fuchun Jiang 686 50 30 0.18 494 Hai Ho 9 34 0.264 51 660 3 Huai 50 185 0.27 50 14 900 Huang He (Yellow) 55 41 0.75 26 1100 2 18.9 30 4670 6 Indigirka 61 61 0.362 42 12.9 3.8 1726 Jubba 17.2 23 0.75 27 5.7 1600 Kaoping 8.5 2615 0.0033 36 33 170 Khatanga 85.3 234 0.364 41 1.7 9.4 1636 Krishna 30 116 0.259 52 64 27 9.5 1290 Liao 16.2 74 0.219 60 41 1350 Limpopo 26 59 0.44 36 6.2 1600 Mahanadi 466 66 0.142 73 60 28 9.7 850 Murray 23.6 7.9 1.06 16 30 (3) 3490 14 Narmada 40.7 394 0.99 125 15 30.7 11.1 1300 Nelson 83 79 1.13 14 21 25 2600 28 Neva 84.4 285 0.282 49 0.82 5.4 74 Nile 83.2 29 0.3 2.87 5 120 17 ***2 [32] [20] 6660 1 Olenek 35.8 163 0.219 59 35 4.06 2270 32 Orange 11 11.4 1 19 89 20 **17 [2.1] 1860 Parnaiba 32.2 99 32 0.325 45 1450 Po 46 699 0.017 15.2 17.3 35 680 Purari 84 46 2750 0.0306 80 21 10.6 630 Red River (Louisiana)a 55.5 23 0.24 54 2075 36 Rhine 69.4 310 0.224 57 3.4 (60.5) (11) 1360 Rhone 59.9 565 0.0196 31 18.2 32 810 Rio Grande (Rio Bravo) 18 21 0.72 0.87 21 ***20 14 2880 19 Senegal 24.4 55 0.44 35 21 *** [1.24] 1430 Shatt el Arab 85 45.7 0.54 33 105 19 ** [18.3] [34] 2760 25 Usumacinta 55.5 1164 0.048 13.3 430 Volta 93 36.8 0.39 40 19 ** [2] 1600 Weser 11.3 231 0.046 0.33 (26.1) (24) 724 Wisla (Vistula) 34.1 164 0.198 63 2.5 (18.9) (31) 1090 Yana 34.3 144 0.238 55 3.5 1.56 872 Values in parentheses indicate rivers with marked increase of TDS fluxes resulting from human impacts.Values in square brackets indicate former TDS fluxes prior irrigation and diversion. Source Meybeck M and Ragu A (1996) River discharges to the oceans. An assessment of suspended solids, major ions and nutrients. Environnement Information and assessment Rpt. UNEP, Nairobi, 250 pp. a Red River upstream of Atchafalaya connexion. Hydrology_FluvialExport125 Table 4 Nutrients and organic carbon concentrations (mg l1 ) in world rivers; DOP, DON and DOC: dissolved organic phosphorous, nitrogen and carbon, respectively River Period SiO2 NNO3 NNH4 PPO4 3 DOP DON DOC Amazon 1990s 6.9 0.14 0.02 0.022 0.015 0.16 5.7 Amur 2.15 0.02 0.021 Arno 19771983 1 1.19 0.5 0.08 1.2 Chang Jiang 19801992 6.5 0.32 0.32 0.02 2.07 Churchill (Hudson) 19791992 1.4 0.01 0.1 0.006 Citarum 19851994 30 0.43 0.53 0.032 Columbia 19791993 9 0.2 0.01 0.014 Congo 1980s 9.4 0.9 0.007 0.24 0.18 9.35 Danube 19791983 4.14 1.5 0.02 Delaware 19791993 3.5 1 0.03 0.04 Elbe 19791990 3.6 1.3 0.39 Evros 200 p km2 ) where urban wastewaters are collected but not appropriately treated (e.g., Scheldt and Seine Rivers in the 1980s): these levels can reach 50100 times the natural background Hydrology _ Fluvial Export 127 levels. A similar pattern is noted for phosphorus, which originates from diffuse agricultural sources and from urban sources (e.g., phosphorus-containing deter- gents). Examples of maximum P levels are given in Table 4 for some Europe an rivers (Arno, Rhine, Seine, Scheldt, Evros) and for the Sakarya River in Turkey. Total phosphorus (TP) is generally measured on unfiltered samples as the sum of PPO4 3 , DOP and particulate phosphorus (PP), sum of organic (POP) and inorganic (PIP). POP originates from soil erosion and is generally linked to POC (POC/POP 22 g g1 ) while PIP originates from the erosion of rock minerals as apatite (PIP is seldom lower than 600 ppm in river suspended matter) and from the adsorption of phos- phates ions onto fine minerals. Both POP and PIP contents increase downstream of urban sewage out- falls. PP is the dominant form of phosphorous during floods and in turbid rivers (e.g., PP in the Huang He exceeds 10 mg l1 because of the erosion of loess). TP budgets based on regular water quality surveys often underestimate the flashy PP inputs during floods. It is therefore recommended that analyses of particu- late phosphorus are performed separately on river SPM and then combined to TSS fluxes to generate PP fluxes. Nutrients Trends and Changes in Stoechiometric N:P:Si Ratios Anthropogenic influences on nutrients sources and sinks can substantially increase the riverine fluxes of NO3 , NH4 , TKN, PO4 3 , TP, or decrease those of dissolved silica. However, the DIC and DOC levels in most rivers are relatively stable on most long-term records (50 to 30 years). As a result the C:N:P:Si ratios in impacted rivers have greatly changed in some well-documented rivers over the last 50 years. Freshwater algae require specific inorganic nutrient ratio (Redfield ratios) for proper nutrition: N:P 16:1 (mol mol1 ) for all algae, and Si:N 1:1 (mol mol1 ) for diatoms, the siliceous algae group. In nat- ural conditions, the Si:N ratio exceeds largely 1:1 value, thus permitting diatom blooms, as dis- solved SiO2 is ranging between 50 and 400 mmol l1 and NO3 between 4 and 25 mmol l1 . In impacted conditions, NO3 is increasing, sometimes by more than a factor of 10, and dissolved silica is retained by algal production within upstream reservoirs thus lowering the downstream SiO2 content by a factor of 2 and more. In such impacted rivers, the Si:N ratio in riverine nutrient fluxes can be lower than 1.0 and silicon becomes the limiting factor of diatom growth. Such Si:N changes have been well demonstrated in the Mississippi River where, according to some authors, they favor alternate primary producers as cyanobacteria particularly in the coastal zone result- ing in seasonal coastal hypoxia. Trajectories of Riverine Fluxes Reflect Pressures Evolution and Water Quality Management In many regions of the world, water quality records and TSS records have been available for more than 30 years (medium-term records), and a few long-term records (50100 years) are available on some rivers (Mississippi, Volga, Rhine, Seine) or from sedimen- tary records in floodplain deposits (for persistent organic pollutants and for metals). The typology of flux trajectories reflects the multi- ple human pressures and the resulting human responses when they are developed (Figure 2, trajec- tories AK). A. A stable evolution is noted for ions, DOC, and nutrients in most pristine rivers (i.e., with- out direct human pressures), although a slow modification of river DOC and DIC fluxes is expected from gradual climate change, because of permafrost melting and CO2 increase. In catchments under pressure such trends are also noted for elements that are the least sensi- tive to human pressure such as Ca2 , Mg2 , and to a lesser extent, to bicarbonate and many Impact Impact Xenobiotics and radionuclides Time Time D F H A C GE B Flux Natural substances Pristine Level I J K 0 0 Figure 2 Typology of long-term riverine fluxes trajectories resulting from the evolution of human pressures and responses on river basins. Adapted from Meybeck M (2001) River basins under Anthropocene conditions. In von Bodungen B and Turner K (eds.) Science and Integrated coastal Management, Dahlem Conference Series,Wiley, 275294. 128 Hydrology _ Fluvial Export particulate metals such as Al, Fe, Co, and V, which have very little impact from most human activities. B. The gradual increase is associated to the pro- gressive development of industries, cities (K , Na , Cl , SO4 2 ), and of industrial fertilizers in agriculture (K , SO4 2 , NO3 , total P). C. A partial retention of dissolved inorganic nutri- ents resulting from algal uptake is noted in many reservoirs (NO3 , PO4 3 , SiO2) (e.g., Mis- sissippi, Danube, Sao Francisco Rivers). D1. The bell-shaped curve characterizes a success- ful and gradual control of undesirable sub- stances as for cadmium, PAHs, and for NO3 , NH4 , and PO4 3 in some Western European and United States rivers. D2. The stepwise improvements (not shown) are observed when major urban or industrial wastewater treatment are installed (few months responses). They are also linked to the reduc- tion, or closure of economic activities following economic crises; e.g., in former socialist countries in Europe, the Elbe and Danube fluxes of nutrients and/or heavy metals, drasti- cally dropped between 1989 and 1990. D3. The stepwise degradation (not shown) is the symmetric evolution resulting from the instal- lation of pollutants sources, or when waste- waters are collected to sewers without proper treatment (e.g., NH 4 increase from urban sewers development). E. The complete particulate matter retention is caused by settling in reservoir, when residence time exceeds 36 months. It is also observed for particulate carbon, nutrients, and pollutants. F. Stabilized fluxes of contaminants and salts (TDS, Cl ) over decades may result from water quality regulation, particularly at inter- national borders (e.g., Colorado River between the United States and Mexico, Rhine River be- tween France and other member states of the Rhine Commission). G. A general decrease of all fluxes is caused by water diversion and/or use for irrigation (e.g., Colorado, Rio Grande, Nile, Ebro, Amu Darya, Syr Darya, Indus, Huang He, Murray). H. Multiple cycles are often noted in long-term trends as a result of the pressures/responses balance (e.g., Thames River organic matter be- tween 1850 and 2000; metal fluxes in the Rhine and Meuse, as reconstructed from sediment archives). I. Fluxes of radioactive substances are very sel- dom addressed or disclosed by water authori- ties. Since 1950, the development of nuclear industries, the nuclear weapon tests in the atmosphere, that peaked in 19621963 in the atmosphere, and their related leaks and accidents (as in 1986 at Chernobyl), have spread artificial radionucleides in all rivers, particularly in the Northern Hemisphere. The typical 137 Cs trajectory in West Europe present a double peak near 1962 and 1986 that is used to date alluvial sediments. J. Total ban (J) is sometimes applied to some substances that do not occur naturally (xeno- biotics) when they are found to be dangerous as for PCBs, used in industrial products and for DDT, banned in 1970, that gradually decreased in West Europe and North America rivers. K. The gradual contamination of other types of xenobiotic substances as pesticides, drugs, some solvents is widely observed. Further Reading Colombani J and Olivry JC (1984) Phenome`nes exceptionnels derosion et de transport solide en Afrique aride et semi-aride. International Association of Hydrological Sciences Publications 144: 295300. Gordeev VV (1983) River Inputs to The Ocean and Features of Its Chemistry, p. 160. Moscow: Nauka (in Russian). Hem JD (1989) Study and interpretation of chemical characteristics of natural water. US Geological Survey Water Supply Paper 2254, USGS Reston, VA. Horowitz A (2003) An evaluation of sediment rating curves for estimating suspended sediment concentrations for sub segment flux calculations. Hydrological Processes 17: 3387 3409. Ittekkot V, Unger D, Humborg C, and TacAn N (eds.) (2006) The Silicon Cycle, SCOPE series 66, p. 275. Washington: Island Press. Kimstach V, Meybeck M, and Baroudy E (eds.) (1998) A Water Quality Assessment for the Soviet Union, p. 611. London: E and FN Spon. Ludwig W and Probst JL (1998) River sediment discharge to the oceans: present-day controls and global budgets. American Journal of Science 298: 265295. Meade RH and Parker RS (1985) Sediment in rivers of the United States. National Water Summary, 1984. Water Supply Paper, vol. 2275, pp. 4060. Reston, VA: US Geological Survey. Meybeck M (2001) River basins under Anthropocene conditions. In von Bodungen B and Turner K (eds.) Science and Integrated coastal Management, Dahlem Conference Series, pp. 275294. Wiley. Meybeck M (2003) Global analysis of river systems: from Earth system controls to Anthropocene syndromes. Philo- sophical Transactions of Royal Society of London B 358: 19351955. Meybeck M (2003) Global occurrence of major elements in rivers. In Drever JI (ed.) Surface and Groundwater, Weathering and Soils. In: Holland HD and Turekian KK (eds.) Treatise on Geo- chemistry, vol. 5, pp. 207223. Amsterdam: Elsevier. Meybeck M and Ragu A (1996) River discharges to the oceans. An assessment of suspended solids, major ions and nutrients. Hydrology _ Fluvial Export 129 Environment Information and assessment Rpt, 250 pp. Nairobi: UNEP. Meybeck M and Vorosmarty CJ (2005) Fluvial filtering of land to ocean fluxes: from natural Holocene variations to Anthropo- cene. Comptes Rendus Geosciences 337: 107123. Meybeck M, Laroche L, Durr HH, and Syvitski JPM (2003) Global variability of daily total suspended solids and their fluxes in rivers. Global Planetary Change 39: 6593. Milliman JD and Syvitski JPM (1992) Geomorphic/tectonic control of sediment discharge to the ocean: the importance of small mountainous rivers. Journal of Geology 100: 525544. Milliman JD (2001) River inputs. In Steele JH, Turekian KK, and Thorpe SA (eds.) Encyclopedia of Ocean Sciences, vol. 4, pp. 24192427. Academic Press. Milliman JD, Rutkowski C, and Meybeck M (1995) River dis- charge to the sea. A global river index (GLORI). LOICZ reports and studies, Texel, ND, pp. 125. Moatar F and Meybeck M (2007) Riverine fluxes of pollutants, towards predictins of uncertainties by flux duration indicators. Comptes Rendus Geosciences Hydrology-Hydrogeology 339: 367382. Peters NE (ed.) (1996) Trends in water quality. Hydrological Processes 10: 127356. Philipps JM, Webb BW, Walling DE, and Leeks GJL (1999) Estimating the suspended loads of rivers in LOIS study area using infrequent samples. Hydrological Processes 13: 10351050. Rabalais NN, Turner RE, Justic D, Dortch Q, Wiseman WJ, and SenGupta BV (1996) Nutrients changes in the Mississippi River and system responses on the adjacent continental shelf. Estuaries 19(2B): 386407. Rode M and Suhr U (2007) Uncertainties in selected river water quality data. Hydrology and Earth System Science 11: 863874. Salomons W, Kremer H, and Turner RK (2006) The catchment to coast continuum. In Crossland CJ, et al. (eds.) Coastal Fluxes in Anthropocene, pp. 145200. Springer. Seitzinger SP, Harrison JA, Dumont E, Beusen AH, and Bouwman AF (2005) Sources and delivery of carbon, nitrogen and phospho- rus to the coastal zone: an overview of global nutrient export from watersheds (NEWS) models and their application. Global Biogeo- chemical Cycles 19. DOI: 10.1029/2005 GB 002606. Syvitski JPM, Vorosmarty CJ, Kettner AJ, and Green P (2005) Impact of human on the flux of terrestrial sediment to the global coastal ocean. Science 308: 376380. Vorosmarty CJ and Meybeck M (2004) Responses of continental aquatic systems at the global scale: new paradigms, new meth- ods. In Kabat P, et al. (eds.) Vegetation, Water, Humans and the Climate, Global Change, IGBP series, pp. 375413. New York: Springer. Walling DE (2006) Human impact on land-ocean sediment transfer by the worlds rivers. Geomorphology 79: 192216. Williams GP (1989) Sediment concentrations versus suspended matter discharge during hydrologic events in rivers. Journal of Hydrology 111: 89106. Relevant Websites USA river water quality and sediment fluxes, US Geological Survey. Gems Water program UNEP, global river water quality data. 130 Hydrology _ Fluvial Export Fluvial Transport of Suspended Solids P Y Julien, Colorado State University, Fort Collins, CO, USA 2009 Elsevier Inc. All rights reserved. Introduction The fluvial transport of suspended solids is of great interest to living communities. It has been known for a very long time that the deposition of fine sediments on flood plains increases the fertility of farmlands. In urban areas, high suspended sediment concen- trations adversely impact the quality of drinking water and increase the operation cost of water treat- ment plants. During floods, the excessive suspended sediment concentrations can also cause major sedimen- tation problems resulting in aggradation, river naviga- tion problems, and changes in river morphology. On the other hand, riverbed degradation from a lack of fine sediment in suspension can also undermine the stability of bridges and river protection structures. Equilibrium Transport of Sediment Suspensions There are two types of sediment sizes that contribute to the suspended sediment load of a river: (1) wash load and (2) bed material load. The difference between wash load and bed material load depends on whether the size fractions can be found in large quantities in the bed. The size fractions that are found in large quantities in the bed are referred to as bed material load. In practice, all size fractions that are finer than the d10 of the bed material will be consid- ered wash load. The wash load does not depend on the sediment transporting capacity of the flow, but depends on the supply of sediment from upstream sources or from the river bank. The quantity of wash load can only be determined from field measurements. Suspended sediment sam- pling is usually done with a point sediment sampler of the type P-61 or P-63. Point sediment samplers are designed to collect sediment through time at a given point along the stream vertical. The sampler weight is the primary difference between the P-61 (100 lb) and P-63 (200 lb) and heavy samplers must be used in deep and fast-flowing rivers. Figure 1 shows a P-63 sampler on the Mississippi River. The bed material load in suspension requires basic knowledge of the properties of the flow and of the transported sediment. In a very simplified form, two main properties describe suspended sediment transport in rivers: (1) the shear velocity of the flow and (2) the settling velocity of the bed material. The shear velocity u ghS0:5 is approximately equal to the square root of the product of gravitational acceleration g, flow depth h, and friction slope S. The settling velocity is a property of the particle in its surrounding fluid. It can be directly calculated from the dimensionless particle diameter d*, which is defined from the particle diameter ds, the specific gravity G of sediment, the kinematic viscosity of the fluid n, and the gravitational acceleration g, as d ds G 1g v2 1=3 1 Simplified calculations are obtained with the grain diameter (m), the kinematic viscosity (n 1 106 m2 s1 ), g (9.81 m s2 ), and G (2.65). The settling velocity o (m s1 ) of a sediment particle in clear water is then calculated from ! 8v ds 1 d3 72 0:5 1 ( ) 2 The ratio of shear velocity u* to settling velocity o determines the primary mode of sediment transport. The bed material can be subdivided into three zones describing the dominant mode of transport: bed load, mixed load, and suspended load. In most rivers, bed load is dominant at values of u*/o less than about 0.4. Note that incipient motion corresponds to u*/o 0.2, which means that the bed material does not move when u* < 0.2o. A transition zone called mixed load is found where 0.4 < u*/o < 2.5 in which both the bed load and the suspended load contribute to the total load. When u*/o > 2.5, most of the sediment load is transported in suspension. Field measurements are necessary to determine the rate of sediment transport. The concentration of suspended sediment in rivers varies with depth. The suspended sediment concen- tration C at an elevation z above the bed for the suspended load can be calculated from the Rouse equation as C Ca h z z a h a !=u 3 where Ca is the concentration at an elevation a above the bed, h is the flow depth, and k is the von Karman constant (k 0.4). The exponent of this equation is called the Rouse number Ro o/ku*, which varies with u*/o. The near-bed concentration can be obtained from point sediment concentration measurements near the bed, or in the lower part of the water 131 column. The Rouse number can be experimentally obtained as the slope of the linear fit to the con- centration profile obtained after a logarithmic trans- formation, as shown in Figure 2. The sediment flux per unit area is the product of the flow velocity and sediment concentration. For instance, the volumetric flux of sediment is obtained from the product of the volumetric sediment concen- tration, the flow velocity, and the unit area. Because the flow velocity and sediment concentration vary with depth and width, it is necessary to integrate the velocity and concentration profiles along the vertical and across the entire width of a river to determine the sediment flux. This integral is very complex and is discussed in detail in Julien (1995). The depth integral of the sediment flux describes the unit sediment dis- charge or amount of sediment being transported per unit channel width qtx. It represents a volume of sediment per unit width. Nonequilibrium Transport of Sediment Suspensions As rivers approach reservoirs, lakes, and estuaries, the reduced sediment transport capacity in the back- water areas causes deposition of the suspended sedi- ment load. Owing to the continuity of sediment, the equation of conservation of mass determines the changes in vertical elevation from settling when there is a decrease in sediment transport in the down- stream direction. This equation of conservation of mass shows that the settling sediment flux in the z direction causes a change in bed surface elevation zb: @zb @t TE 1 p0 @qtx @x 4 The porosity p0 depends on the specific weight of sediment deposits and is approximately 0.43 for sand-bed rivers. The trap efficiency TE describes the fraction of sediment that would deposit in a given river reach of length X. It is therefore a measure of how much sedimentation could take place in backwa- ter flow conditions. Trap efficiency is a function of the reach length X, the river width W, the flow dis- charge Q, the mean flow velocity V, and the settling velocity o as TE 1 exp X! hV 1 exp WX! Q 5 This relationship for the trap efficiency of sediment can be useful. At a given flow discharge, the trap efficiency remains very small for very short reaches and for very fine sediment particles (low o). Under Figure 1 Suspended sediment sampling on the Mississippi River. 102 10 101 101 102 1 1 10 102 1 1 1 Ro = 0.63 Ro= 0.49 Run 19 Vanoni, 1946 h=0.236ft d50=0.10 mm k =0.33 Run 55 h=0.590ft d50 =0.10mm k =0.34 Run S-16 Einstein and Chien, 1955 h=0.390ft d50 =0.274mm k =0.18 Ro= 1.86 Hyper-conc.Suspension 103 Concentration C (g/l) (h-z)/z Figure 2 Examples of sediment concentration profiles (from Julien, 1995). 132 Hydrology _ Fluvial Transport of Suspended Solids changes in sediment transport capacity in the down- stream direction, the trap efficiency describes a greater potential for coarse sediment to deposit. It is also interesting to note that the trap efficiency at a given reach length and flow discharge increases with increasing sediment size o and channel width W. It is therefore noticeable at a given discharge that river widening will induce settling of suspended sediment (Julien, 2002). When calculating the trap efficiency of silt and clay particles in backwater areas like reservoirs and estu- aries, careful consideration must also be given to density currents and possible flocculation. Floccula- tion of silts and clays is a complex subject, but in its essence, the settling velocity of floc of silts and clays is typically around 0.6 mm s1 . The settling velocity of flocs increases with floc size but will rarely exceed 5 mm s1 . As an example to illustrate the concepts covered in this article, consider the Rhine River data from Julien (2002). The flow depth is approximately 10 m, the main navigable channel constrained between a series of dikes is about 260 m wide, the mean flow velocity is 1.68 m s1 , and the friction slope 13.2 cm km1 . The sediment concentration at mid depth is 38 mg l1 , and the near-bed concentration is 400 mg l1 at a distance of 0.5 m above the river bed. If the grain diameter of the sediment in suspension is 0.2 mm, the following parameters can be calculated from the methods covered in this article: (1) the shear velo- city obtained from u ghS0:5 is approximately u* 0.11 m s1 ; (2) the dimensionless particle diame- ter is approximately 5 from eqn [1] and the settling velocity from eqn [2] is o 0.027 m s1 ; (3) the ratio u*/o 4.2, and the Rouse number is 0.59 assuming k 0.4, thus most of the sediment is transported in suspension; (4) the suspended sediment concentra- tion 1 m below the free surface is 19 mg l1 obtained from Ca 400 mg l1 at a 0.5 m, h 10 m, and the concentration at z 9 m from eqn [3]; and (5) the trap efficiency over a reach length of 500 m from eqn [5] is TE 0.55, which means that about half the suspended sediment load would deposit within half a kilometer if the transport capacity of this river would be suddenly reduced. This example is quite instructive because most of the suspended sediment load would deposit very rap- idly despite the fact that most of the sediment is fine and transported in suspension. The high TE indicates that most of the sediment would also easily be trapped on the flood plain within short distance of the main channel during major floods. This river would be very dynamic and could change morphol- ogy if it were not constrained with a series of dikes. Finally, the suspended sediment concentration near the free surface is only 19 mg l1 compared with 400 mg l1 near the bed, and water intakes should definitely be located near the free surface. Further Reading Julien PY (1995) Erosion and Sedimentation, 280p. New York: Cambridge University Press. Julien PY (2002) River Mechanics, 434p. New York: Cambridge University Press. Hydrology _ Fluvial Transport of Suspended Solids 133 Streams E Wohl, Department of Geosciences, Colorado State University, Ft. Collins, CO, USA 2009 Elsevier Inc. All rights reserved. Introduction Every point on the Earths landmass lies within a drainage network formed of stream channels tribu- tary to one another that eventually drain to an inland reservoir or to an ocean. The spatial arrangement of channels into a drainage network, the water and sedi- ment moving from hillslopes and down streams, and the geometry of streams, all reflect climatic and geo- logic factors within the drainage basin. Spatial Organization of Streams in Drainage Networks A drainage network includes all the stream channels that drain toward a reference point. The network is bounded by a topographically defined drainage divide; precipitation falling on the far side of the divide flows down slope into an adjacent drainage network. A drainage network begins with first-order streams to which no other stream is tributary. In the most com- monly used method of stream orders, a second-order stream begins at the junction of two first-order streams, a third-order stream begins at the junction of two second-order streams, and so on (Figure 1). Patterns of drainage networks. The spatial distri- bution of streams within the network can be descrip- tively classified using terms including dendritic, rectangular, radial, and others. Dendritic drainages are the most widespread, taking their name from a resemblance to the outline of a tree (Figure 2). A dendritic drainage is commonly interpreted to re- flect a relatively homogeneous substrate of moderate down slope gradients. A rectangular drainage, in con- trast, has many right-angle tributary junctions that reflect a strong underlying control, such as joints in the bedrock, which influences the location of stream channels. A radial drainage network more likely reflects the underlying topographic control, such that individual streams radiate outward and down from a central high point such as a volcanic cinder cone. This descriptive classification for drainage net- works is useful because it is readily apparent in aerial photographs, topographic maps, or digital elevation models of a landscape, and because the categories of the classification imply something about the geo- logic controls on the spatial arrangement of stream channels across a landscape. Drainage density. Drainage networks can be quan- titatively described using parameters such as drainage density, which is the ratio of total length of streams within a network to the surface area of the network (stream km/km2 of drainage area). Drainage density reflects climatic controls, substrate on which the drainage network is formed, and age of the drainage network. The highest values of drainage density tend to occur in semiarid regions and in the seasonal tro- pics. In each of these regions, high-intensity rainfalls create sufficient erosive force to overcome the surface resistance of hillslopes and form stream channels. High values of drainage density can also be associated with very steep topography, with erodible substrates, and with patterns of land use such as deforestation that reduce hillslope resistance to surface erosion. Drainage networks initially form relatively rapidly on newly exposed landforms such as glacial or volca- nic deposits. The rate of increase in drainage density then levels off with time as the network becomes fully integrated and the spacing of stream channels reflects the minimum surface area needed to produce sufficient runoff to support a channel. Formation of stream channels. A stream channel can form as the result of either surface or subsurface processes, or some combination of the two. Hetero- geneities in the surface and subsurface properties of hillslopes create zones of preferential flow during downslope movement of water. As water preferen- tially concentrates on the surface, the force exerted against the surface by the flowing water increases proportionally to the depth of the water. A self- enhancing feedback occurs such that an initial surface irregularity slightly concentrates surface flow on the hillslope, and the slightly deeper flow in this irregu- larity exerts more erosive force against the surface, thus deepening the irregularity, which then concen- trates yet more flow as it widens and deepens. Even- tually, the irregularity creates a spatially continuous downslope flow of water in the form of a rill. If one of a series of parallel rills enlarges faster than the neighboring rills, the master rill creates a secondary side slope between its channel and that of adjacent rills. This secondary slope facilitates shifting of the smaller rill so that it becomes tributary to the larger rill, and a drainage network begins to form. An analogous process occurs in the subsurface, where differences in porosity and permeability create localized zones of greater flow that dissolve or 134 physically erode material to create subsurface cav- ities. These cavities can form surface channels if the overlying material collapses into the cavity. The resulting sapping and piping networks have distinc- tive channels in which surface flow begins abruptly at an amphitheater-shaped depression in the ground surface. Because the area of hillslope contributing flow to a stream channel increases downslope, thresholds for erosion and channel formation can be crossed at downstream portions of a slope first, and the stream channels then erode headward as the network of channels enlarges. If one set of channels erodes head- ward more rapidly than an adjacent network, the former channels can erode through the drainage divide and capture a portion of the adjacent network. This situation is occurring presently at the Casiquiare Canal, a naturally occurring channel along which a portion of the headwater drainage of the Amazon River of South America is capturing some of the headwater drainage of the adjacent Orinoco River. The point along a hillslope at which stream chan- nels begin to form depends on factors such as char- acteristics of precipitation, infiltration capacity of the surface, and erosional resistance of the surface (Figure 3). Regions with intense rainfall, low infiltra- tion capacities, and highly erodible surfaces can have drainage networks that start very close to the crest of hillslopes, whereas other areas with less intense precipitation, higher infiltration, or greater surface resistance may have channel networks that begin much farther downslope. Sources of Flow in Streams The ultimate source of water flowing in any stream is snowmelt, rain-on-snow, or rainfall. Snowmelt gener- ally produces regular seasonal patterns of stream flow during the onset of warmer temperatures when snow packs have accumulated during the winter melt. Snowmelt tends to be an important source of stream flow at higher latitudes and higher altitudes. Snow and rainfall can also enter streams after having been stored as ice in glaciers or icefields for periods of up to thousands of years. As with other forms of snow- melt, glacier melt is most pronounced during warmer seasons of the year, but can persist throughout the warm season (unlike snowmelt, which tends to be most pronounced during the early part of the warm season). 1st order stream 2nd order stream 3rd order stream 4th order stream Drainage divide 1 1 1 2 2 3 2 3 4 2 2 3 22 Figure 1 Schematic drawing of a drainage network, showing the ordering of streams, and delineation of the drainage divide. Figure 2 Dendritic drainage network formed on a gently sloping surface with homogeneous underlying sediment, northwestern Australia. The trees in the photo are approximately 810 m tall. Figure 3 Bedlands topography in Death Valley National Monument, California. Channels begin very close to the ridge crests, as can be seen most clearly along the dark brown ridge crest running across the lower third of the photograph. Hydrology _ Streams 135 Rain-on-snow occurs when warmer temperatures cause rain to fall directly onto snow packs that have not yet completely melted. The warmer temperatures increase the melt rate of the snow which, when combined with rainfall, can create high rates of run- off and associated flooding. Rain-on-snow floods are particularly prevalent in low-to-moderate elevation catchments in coastal mountain ranges at middle latitudes. The intensity, duration, and spatial extent of rain- fall vary greatly among different types of climatic circulation patterns that generate rainfall. Convective storms create very intense rains that cover small areas (1102 km2 ) for periods of up to a few hours. Frontal storms that last for days can extend across 104 km2 . The most extensive rains are associated with cyclonic storms such as hurricanes that last for days to weeks and monsoonal circulation patterns that last for months at a time. Both cyclonic and monsoonal storms can cover large areas of 105 107 km2 . Convec- tive storms can generate enormously large stream flows within small drainage basins, but the effects of a small storm can be mitigated in large drainage basins where substantial portions of the basin remain unaffected by the storm. The more extensive frontal, cyclonic, and monsoonal storms can produce floods across much larger drainage basins. The distribution of different types of precipitation reflects global-scale atmospheric circulation patterns, as well as regional topographic influences on the move- ment of air masses that bring moisture over a drainage basin. The regions with the greatest annual precipita- tion mostly lie within 30 north and south of the equa- tor, where air masses moving across the warm surface of the tropical oceans pick up tremendous amounts of water vapor that is then transported inland to fall as precipitation. Smaller areas of very high precipitation can occur at higher latitudes where a mountain range forces moisture-bearing air masses to rise higher into the atmosphere, causing the water vapor within the air masses to condense and fall as precipitation, or where proximity to an ocean surface with relatively warm temperatures facilitates evaporation and inland trans- port of moisture from the ocean. Convective storms, which involve localized strong updrafts, are most com- mon at latitudes 10 N10 S. Frontal storms occur when the boundary between two air masses with dif- ferent densities passes over a region and brings wide- spread precipitation. Monsoonal storms are associated with seasonal reversals of winds that draw moisture from adjacent oceans over land masses. Cyclonic storms, which have a strong rotational component, occur in two broad bands at approximately 10 50 north and south of the equator. Stream flow can also be dramatically affected by the failure of a natural or human-built reservoir. Lakes created when a landslide or debris flow blocks a stream commonly burst within a few days as the blockage is overtopped or weakened by seepage and piping. Water ponded upstream from glacial mor- aines or underneath glacial ice can also empty cata- strophically when the moraine is overtopped or weakened within, or when the confined water builds sufficient pressure to lift the overlying glacial ice. Human-built fill and concrete dams can also fail by being overtopped or undermined. In each of these cases, sudden release of the ponded water initiates a catastrophic flood that continues until the reservoir is drained below the level of the remaining portions of the dam, or until the glacial ice once again shuts off the drainage path. Patterns of stream flow reflect global and regional atmospheric circulation patterns and topography, as well as drainage area. Rivers in the equatorial and tropical latitudes commonly have the largest mean flow per unit drainage area because of the greater amounts of precipitation at these latitudes. Peak flow per unit drainage area tends to be greatest in relatively small rivers because the entire drainage area can be contributing runoff during intense precipita- tion events. Seasonal and interannual variability of flow tend to be largest in arid and semiarid regions, and in the seasonal tropics. Movement of Water into Stream Channels Precipitation falling across a landscape moves down- ward along various paths from hillslopes into stream channels. Precipitation can remain at the ground sur- face and move downslope relatively quickly as runoff or Hortonian overland flow. Precipitation can also infiltrate the ground surface and move downslope more slowly. Throughflow occurs when subsurface flow moves within the upper, unsaturated layers of sediment. Although the matrix as a whole remains unsaturated, concentrated zones of flow in pipes or macropores, or temporarily saturated zones, are par- ticularly effective in moving water downslope into streams relatively rapidly. If the infiltrating water reaches the deeper, saturated layers of the subsurface, the water moves downslope with ground water. Hill- slopes tend to be heterogeneous environments as a result of small-scale variations in surface topography and the porosity and permeability of subsurface materials. Throughflow moving downslope can con- centrate in topographic irregularities and zones of limited porosity and permeability along the hillslope 136 Hydrology _ Streams and return to the surface to move downslope as satu- ration overland flow. Overland flow and shallow, concentrated subsurface flow in pipes or macropores usually move downslope most rapidly, and these sources of runoff are together sometimes referred to by the descriptive term quickflow. Other forms of throughflow, as well as groundwater flow, move at slower rates (Figure 4). The distribution of water among these four basic flow paths commonly varies across time and space. Rainfall that initially produces throughflow can sub- sequently create overland flow, for example, if infil- tration capacity declines following prolonged rainfall or an increase in rainfall intensity. Convex portions of a hillslope can produce dominantly throughflow, whereas concave portions of the slope have satura- tion overland flow during the same rainstorm. Spatial and temporal variability in the downslope movement of water reflects the characteristics of precipitation inputs and hillslope pathways. Pre- cipitation intensity and duration exert particularly important influences on downslope movement of water. Higher intensities of precipitation are more likely to overwhelm infiltration capacity and produce overland flow, but prolonged precipitation at any intensity has the potential to exceed infiltration capacity. Hillslope characteristics including vegetation cover, downslope gradient, and the porosity and permeabil- ity of materials at the surface and in the subsurface also strongly influence the downslope movement of water. Vegetation cover intercepts some precipitation, allowing snow or rain to evaporate or sublimate directly from the plant without reaching the ground, or reducing the force of impact when raindrops bounce from the plant onto the ground. Vegetation also sheds dead leaves and branches that can build up over time in a surface layer of duff with high infiltration capacity. Linear cavities left in the subsur- face when plant roots die and decay can create macro- pores that facilitate rapid downslope movement of water in the subsurface. Steeply sloping surfaces can create large subsurface pressure differences that facilitate more rapid subsurface flow. Hillslope mate- rials with high porosity (percent of void space) and permeability (interconnectedness of void spaces) also facilitate rapid infiltration and downslope movement of subsurface water. Porosity and permeability can- result from spaces between individual grains in unconsolidated materials. Sand and gravel tend to have lower porosity but higher permeability than finer silt and clay-sized particles, with the result that sand and gravel commonly have higher infiltration and downslope transmission of water. Larger cavities in the form of pipes or macropores in sediments, or fractures in bedrock, also facilitate downslope flow. Pipes and macropores can result from biological pro- cesses including animal burrows or decayed plant roots. They can also form by erosion when subsurface flow concentrated above a less-permeable unit builds sufficient force to remove particles and create a continuous subsurface cavity (Figure 5). In general, hillslopes with limited vegetation cover or surfaces disturbed by humans are likely to have Evapo- transpiration (up to 50% for forests) Precipitation Ground water Water table Soil profile Zone of percolation Ground water ( 1108m/h) Infiltration capacities (22500mm/h) Hortonian overland flow (50500 mm/h) Saturation overland flow (convergent zones) Throughflow (different levels) Figure 4 Schematic side view of hillslope illustrating four basic downslope pathways of water (italicized) and range of rates of movement. Hydrology _ Streams 137 more overland flow, whereas subsurface flow paths become more important with greater vegetation cover and deeper, more permeable soils. However, even a catchment with continuous, dense forest cover can have rapid downslope transmission of pre- cipitation during conditions of high rainfall intensity or where thin soils and preferential subsurface flow paths such as pipes and macropores are present. Movement of Sediment into Stream Channels Sediment transported downstream can come from adjacent hillslopes, floodplains, and valley bottoms, and from erosion of the bed and banks within the stream. Hillslope sediment enters streams via gradual processes of slope erosion that occur through slope wash, soil creep, rill erosion, and other movements of individual sediment particles. Large volumes of sedi- ment can also be introduced to streams during mass movements such as landslides, debris flows, and rock falls. Mass movements become progressively more important sources of sediment to streams where adja- cent slopes are steeper and where episodic triggers such as intense rainfalls, seismic shaking, or wildfires periodically destabilize the hillslopes. Mass move- ments are particularly important in bringing sediment directly into headwater streams in mountainous ter- rains where narrow valley bottoms and spatially lim- ited floodplains leave little storage space for sediment between the hillslopes and stream channels. Moun- tainous terrains around the world produce an esti- mated 96% of the sediment that eventually reaches the ocean basins, but occupy only 70% of the land area within river basins (Figure 6). Floodplains adjacent to streams provide a very important source of sediment to streams, although the dynamics of sediment movement between streams and floodplains are spatially and temporally com- plex. Overbank flows that inundate floodplains can Figure 5 Channel segments affected by subsurface piping along Cienega Creek in central Arizona. As subsurface pipes enlarge, the overlying sediment collapses into the cavity (upper photo) until eventually the collapse becomes longitudinally continuous, leaving a deeply cut channel with nearly vertical banks (lower photo). 138 Hydrology _ Streams deposit large volumes of sediment as particles carried in suspension settle from waters that move more slowly across floodplains. This sediment can remain in storage on the floodplain for periods ranging from hours to tens of thousands of years. The floodplain changes from a sink to a source of sediments when processes such as lateral stream migration cause the channel to move across the floodplain and reintro- duce sediment from the floodplain into the stream. The rate and manner of floodplain deposition and erosion vary with stream type. Meandering channels tend to erode the outer portion of each meander bend, for example, creating more predictable directions and rates of floodplain erosion, whereas braided channels can shift abruptly back and forth across the valley bottom in a much less predictable fashion. Because many nutrients and contaminants travel adsorbed to silt and clay particles, the storage and remobilization of floodplain sediments can exert a strong influence on stream chemistry and ecological communities. Erosion of the stream bed and banks provides a third primary source of sediment in stream channels. This form of erosion can be very temporary; most floods erode the channel boundaries while discharge is increasing, but then redeposit sediment during the falling limb of the flood when discharge is decreasing once more. Bed and bank erosion can also be more sustained when a stream is progressively incising downward in response to an increase in discharge, a decrease in sediment supply from other sources, or a drop in the base level (the lowest point to which the stream flows; the ocean is the ultimate base level). Most streams are continually adjusting to changes in water and sediment supply and base level. As a result, erosion of stream bed and banks is also continual in most streams, although this erosion may be balanced by deposition elsewhere along the stream, as when a migrating meander bend has ero- sion of the outer bend and simultaneous deposition of a point bar on the inner bend. Characteristics of Flow in Streams Hydrology of streams. One of the simplest ways to characterize flow in a stream channel is to quan- tify discharge through time. Discharge, usually ex- pressed in cubic meters or cubic feet per second, is volume of flow per unit time. Discharge is calculated by measuring the velocity, or rate of flow (meters per second) within a cross-sectional area (square meters) calculated from mean width and depth of the flow. Continuous records of discharge come from stream- gaging stations where calibrated rating curves are used to convert measurements of stage, or flow depth, into discharge. These continuous records can then be used to construct a hydrograph, which is a plot of discharge versus time. A flood hydrograph represents a discrete event, whereas an annual hydrograph represents vari- ations in discharge over the course of a year (Figure 7). Hydrographs can be used to differentiate base flow, which is the relatively constant input of water to the stream from groundwater sources, from runoff that results from snowmelt and rainfall entering the stream via throughflow and overland flow. The shape of the hydrograph can be characterized by the relative steep- ness of the rising and falling limbs of higher flow, as well as the magnitude, duration, and frequency of occurrence of higher flow. Hydrograph shape is influenced by the precipita- tion mechanism, the paths of downslope movement of water, and location within the drainage network. Higher intensity precipitation and greater overland flow produce more peaked hydrographs. Convective rainfall that results in Hortonian overland flow will produce a flash flood, for example, whereas snow- melt or prolonged gentle rain created by a low- pressure trough that results in throughflow will produce a lower magnitude, and a more sustained flood peak. Other factors being equal, smaller basins tend to have more peaked hydrographs because the close connections between hillslopes and streams, the narrow valley bottoms with limited floodplains, and the relatively short stream networks all facilitate rapid movement of water through the channel net- work. Larger basins that have broad, longitudinally continuous floodplains and longer travel times from headwaters to downstream measurement points pro- duce floods that are less peaked and more sustained. Longer travel times occur both because water must Figure 6 A massive rockfall coming from the right enters a stream channel in the Nepalese Himalaya, causing the channel to become braided downstream. Hydrology _ Streams 139 travel through a longer network of stream channels, and because more of the water travels slowly across floodplains rather than being concentrated within stream channels. The attenuation of flood discharges across floodplains is critical for depositing sediment and nutrients on floodplains, reducing flood hazards by limiting the magnitude of flood peaks, limiting channel erosion during floods by expending some of the flow energy, and nourishing floodplain wetlands and other ecosystems. Flow duration curves, which plot magnitude of discharge versus the percent of time that discharge occurs, provide another means of characterizing the distribution of water in a stream through time. These curves graphically represent the variability of stream- flow by the shape of the curve. Curves with low slope and high minimum values indicate a more ephemeral character and a quicker response to precipitation events. Flow duration curves are most frequently used for determining potential water supply for power generation, irrigation, or municipal use. Flood-frequency curves indicate the average length of time, or recurrence interval, between floods of a similar magnitude. These curves are commonly used for predicting or mitigating flood hazards and for restoring streams in which the distribution of flow has been altered by dams, diversions, or other forms of flow regulation. Estimation of the recurrence inter- val of very large, infrequent floods, such as those that occur on average every hundred years, is particularly difficult because flood-frequency estimation is based on extrapolation from gage records that are commonly less than a century in duration. Supplementing gage records using information from historical, botani- cal, or geological sources can substantially improve the accuracy of estimated recurrence intervals for very large floods, or for streams with no gaging records. Hydraulics of streams. Water flowing within a stream channel is converting potential energy to kinetic energy and heat. The amount of potential energy available for this conversion depends on the vertical drop as the water moves downstream, and on the mass of water moving downstream. Kinetic energy can be expended in overcoming external and internal resistance, and in transporting sediment. External resistance comes from roughness along the bed and banks of the stream. Individual grains that protrude into the flow create external roughness, as do bedforms such as ripples and dunes, coarse woody debris in the stream, irregularities in the channel banks, and downstream variations in channel shape such as meander bends or alternating pools and rif- fles. Internal resistance occurs when individual fluid elements do not follow all parallel flow paths and 50 100 150 0 200 Days since January 1 Days since January 1 0 100 200 300 0 100 200 300 Dailymeanstreamflows(ft3/s)Dailymeanstreamflows(ft3/s) 50 100 150 200 0 250 Snowmelt Rainfall Base flow Rising limb Falling limb Peak flow Runoff Time Discharge Figure 7 An idealized flood hydrograph (left), showing base flow, storm runoff (gray shading), and rising and falling limbs. Sample annual hydrographs (right) for a snowmelt-runoff stream (top) and a rainfall-runoff stream (bottom). 140 Hydrology _ Streams move at the same velocity (laminar flow), but instead move at different rates with components of vertical and lateral movement as well as downstream move- ment (turbulent flow). Flow in all natural stream chan- nels is turbulent to some extent because the water moving along the stream bed and banks encounters more external resistance and moves more slowly than water toward the top center of the stream (Figure 8). Sediment transport in streams. Sediment can be transported in solution within streams. This dissolved or solute load constitutes a greater proportion of sedi- ment transport during periods of base flow, when water that has moved slowly through the subsurface and had longer periods of time to react with the sur- rounding matrix, constitutes a greater proportion of stream discharge. Dissolved load is also relatively large for streams draining rocks such as limestone, which is susceptible to chemical weathering, and for streams in tropical regions that tend to have higher rates of chemical weathering for all types of rocks. Sediment that is not dissolved in stream water can move in suspension within the water column or in contact with the stream bed. Washload is the finest portion of the suspended material, predominantly silts and clays that do not form a substantial portion of the sediment on the streambed. Washload requires so little energy to be transported that it tends to remain in suspension for hours or days even in areas of still water. Suspended load refers to the slightly coarser sands and pebbles that alternate between per- iods of moving in suspension and periods of moving along the bed and can settle from suspension rela- tively rapidly when velocity decreases. Bedload moves in nearly continuous contact with the streambed as larger particles roll, slide, and bounce downstream. Because the larger particles that constitute suspended and bedload require greater amounts of energy to move, much of this transport occurs during floods (Figure 9). Glossary Bedforms Regularly repetitive longitudinal alterna- tions in streambed elevation, such as pools and riffles, steps and pools, or dunes. Bedload Sediment moving in nearly continuous contact with the streambed. Dissolved load Sediment transported in solution by stream flow. Drainage density A measure of the total length of stream channels per unit area of the drainage basin. Laminar flow Turbulent flow Plan view of flow lines in a stream channel Downstream view of velocity distribution in a stream channel Figure 8 Simplified illustration of hydraulics in a natural channel. The plan view drawings illustrate laminar flow, in which all streamlines are parallel and water moves at equal rates, and turbulent flow, in which streamlines move at different rates, and flow has components of movement laterally across the channel and vertically within the channel, as well as downstream. The downstream view illustrates a natural channel with a slightly irregular cross-sectional form and sources of external resistance along the channel boundaries, including wood (right), cobbles and boulders (center), and submerged vegetation (left). The resulting isovels, or contours representing equal velocity distribution, are shown as dashed lines. The slowest velocities are along the sides and bottom of the channel. Figure 9 A flood from the Paria River (mouth at upper left) joins the Colorado River at Lees Ferry, Arizona. The Colorado River, at right, flows relatively clear, whereas the Paria carries high concentrations of suspended sediment. Hydrology _ Streams 141 Drainage divide A topographic high point or line that delineates the boundaries of a drainage network. Drainage network An integrated group of stream channels that drain toward a common point. External resistance Hydraulic resistance created by the channel boundaries. Floodfrequency curve A plot of flood magnitude versus recurrence interval. Flow duration curve A plot of discharge magnitude versus the percent of time that discharge occurs. Glacier melt Runoff created when glacial ice melts. Groundwater flow subsurface flow that occurs below the water table, or zone of saturation. Hydraulics The mechanical properties of liquids; for rivers, these properties are described by vari- ables such as velocity. Hydrograph A plot of discharge versus time. Internal resistance Hydraulic resistance created by differences in the rate and direction of movement of individual fluid elements within a channel. Laminar flow Individual fluid elements follow par- allel flow paths and move at the same velocity. Overland flow (Hortonian, saturation) Water moving across the ground surface; Hortonian over- land flow has no infiltration, whereas saturation overland flow results from water that briefly infil- trates to shallow depths and then returns to the surface as the subsurface becomes saturated. Piping The processes whereby preferential flow in the unsaturated zone creates longitudinal cavities in the subsurface. Rainfall Liquid precipitation that results from dif- ferent types of atmospheric circulation patterns. Rain-on-snow Rain falling directly on a snowpack, which increases the rate of snowmelt. Reservoir failure Collapse of a dam built by natural processes such as landslides, or by humans; the collapse results in rapid drainage of the water ponded behind the dam. Rill Channels that have no tributaries. Sapping The processes whereby preferential flow in the saturated zone creates longitudinal cavities in the subsurface. Sediment transport The movement of sediment in channels, includes dissolved, wash, suspended, and bedload. Snowmelt Runoff created when snowfall or snow- pack melts. Suspended load Particulate material moving in sus- pension in stream flow and of a size that can settle relatively rapidly when velocity decreases. Throughflow Subsurface flow that occurs above the water table, or in the unsaturated zone. Turbulent flow Individual fluid elements move at different rates and exhibit lateral and vertical components of movement as well as moving down- stream. Washload The smallest sizes of particulate material moving in suspension in stream flow; usually clay- and silt-sized particles that do not form a substan- tial portion of the sediment on the streambed. See also: Currents in Rivers; Fluvial Export; Fluvial Transport of Suspended Solids; Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes. Further Reading Milliman JD and Syvitski JPM (1992) Geomorphic/tectonic control of sediment discharge to the ocean: The importance of small mountainous rivers. The Journal of Geology 100: 525544. Poff NL, Allan JD, Bain MB, et al. (1997) The natural flow regime. BioScience 47: 769784. House PK, Webb RH, Baker VR, and Levish DR (2002) Ancient Floods, Modern Hazards: Principles and Applications of Paleo- flood Hydrology. American Geophysical Union Press. Hirschboeck KK (1988) Flood hydroclimatology. In: Baker VR, Kochel RC, and Patton PC (eds.) Flood Geomorphology, pp. 525544. New York: John Wiley and Sons. Knighton D (1998) Fluvial Forms and Processes: A New Perspec- tive. Oxford University Press. Leopold LB, Wolman MG, and Miller JP (1964) Fluvial Processes in Geomorphology. Freeman and Company. Wohl EE (2000) Mountain Rivers. American Geophysical Union Press. Relevant Websites U.S. Geological Survey floods. Federal Emergency Management Agency floods. National Oceanic and Atmos- pheric Administration floods. Dartmouth Flood Observatory. U.S. Geological Survey surface- water records. National River Restoration Science Synthesis. Willamette Basin (Oregon) explorer. U.S. Geological Survey StreamStats. 142 Hydrology _ Streams Rivers P A Bukaveckas, Virginia Commonwealth University, Richmond, VA, USA 2009 Elsevier Inc. All rights reserved. What is a River? There is no strict definition to distinguish rivers from streams and therefore the designation river encom- passes flowing waters of widely varying size. Flowing waters may be ranked in size by various metrics that include discharge (glossary), catchment area, and length of channel. For example, the discharge of the Amazon River is six orders of magnitude greater than that of a small river. This range of variation is compa- rable with the range in volume observed among lakes worldwide. Rivers are sometimes defined as non- wadeable flowing waters since this delineation has practical implications for the way sampling activities are carried out. Along the continuum from headwater streams to large rivers, there are gradients in channel slope, width, and depth. Idealized gradients in geomor- phology provide a basis for understanding differences in the structure and functioning of streams vs. rivers. For example, the greater width of river channels reduces the importance of riparian inputs while greater depth lessens the influence of benthic processes. Rivers in their natural settings exhibit complex geomorpholo- gies that give rise to a rich variation in channel form and function and provide diverse habitats for aquatic biota. Hydrology and Geomorphology Water Sources and Discharge Water sources to rivers are principally surficial inputs via tributary streams (Table 1). Owing to their small surface area, direct atmospheric inputs are usually minor though ground water is important in some settings. For comparisons among river basins, dis- charge is converted to an areal water yield by dividing the volume of discharge by the area of the drainage basin. Water yields vary widely depending on the amount of precipitation relative to evapotranspira- tion (glossary). South American rivers such as the Amazon and Orinoco are notable for their high water yields, exceeding 1000 mm year1 (Table 2). Arid and semiarid regions are characterized by low precipitation relative to evapotranspiration and water yields less than 100 mm year1 . Arid regions occupy about one-third of the worlds land area, including portions of several major river basins such as the Murray-Darling (Australia), Colorado (North America), Nile (Africa), and Ganges (Asia) Rivers. Variation in river discharge arises from short-term, seasonal, and long-term variability in precipitation and evapotranspiration within the drainage basin. Over short time scales (daysweeks), discharge is affected by rain events associated with frontal pas- sage. Though infrequent in occurrence, event-related discharge may account for a large proportion of the annual total. The frequency and magnitude of storm events is therefore an important factor influencing interannual variation in discharge. Event-driven and seasonal variations are superimposed upon long-term (decadal-scale) climatic cycles (e.g., El Nino Southern Oscillation), which may bring about extended peri- ods of above- or below-average discharge. The com- bined effects of climatic variations occurring over multiple time scales results in a wide range of dis- charge conditions, which may exceed three orders of magnitude for a given site. Variation in discharge is typically larger that the variation in the concentration of dissolved and particulate substances such that the export of materials from the basin (flux rate) is prin- cipally determined by discharge. Seasonal variation in rainfall and evapotranspira- tion give rise to predictable annual patterns in river discharge that are characteristic of climatic regions (Figure 1). In temperate-humid climates, rainfall may be distributed relatively uniformly throughout the year but seasonal changes in evapotranspiration give rise to variation in discharge. Warmer months are associated with high evapotranspiration, resulting in less runoff from the catchment and lower river dis- charge relative to colder months. Snowmelt may also contribute to a spring discharge pulse in climates that allow for winter accumulation of snow (including tropical rivers with mountainous catchments). The north-flowing rivers of Canada and Russia are repre- sentative of this hydrologic regime in exhibiting high year-round discharge but with a pronounced winter-spring peak. In tropical-humid climates, evapotranspiration is less variable throughout the year but rainfall is often strongly seasonal, particu- larly in regions affected by monsoons. Wet seasons are associated with elevated river stage and discharge and may be accompanied by extended periods of floodplain inundation. Most South American and African rivers are representative of the tropical uni- modal hydrologic regime, which is characterized by an extended period of elevated discharge and flood- plain inundation during the rainy season. Arid and 143 semiarid regions occur in both temperate and tropical climates and occupy about one third of the worlds land area. They are characterized by low precipitation relative to evapotranspiration and include portions of several major river basins, including the Murray- Darling (Australia), Missouri (North America), Nile (Africa), and Ganges (Asia) Rivers. River basins in arid regions exhibit sustained periods of low discharge interspersed with short periods of elevated discharge. For example, the Murray-Darling River is fed by infre- quent summer monsoons which, coupled with high rates of evapotranspiration, result in an annual dis- charge equivalent to only 3% of annual rainfall. Large river basins may span climatic and topo- graphic regions and exhibit complex hydrologic regimes. For example, the Rhone is a snowmelt- dominated river in its upper, mountainous sections but is influenced by a Mediterranean climate in its lower course. The river exhibits a complicated flow regime with low discharge periods shifting from win- ter in the upper course to autumn in the lower course and floods occurring in all seasons. Despite the problems inherent in categorizing this continuum of variation, hydrologic regimes are useful for facilitat- ing comparisons among river basins (e.g., in response to land-use and climate change effects). Flooding Rivers experience large and rapid fluctuations in sur- face water elevation (i.e., stage) in response to run- off. The rate and magnitude of rise in river stage is dependent in part on the morphometry of the channel (Figure 2). Low banks enable the river to escape the active channel and inundate lateral areas (floodplain). During flooding, the widening of the river lessens the stage response to runoff and reduces water velocity because the force of the water is distributed over a wider area. Flood-prone rivers are common in both temperate and tropical climates and exhibit consider- able variation in the extent, timing, and frequency of flooding events. In some settings (e.g., Amazon River) the annual flood pulse is a defining feature of the riverscape, important not only to the life cycles of riverine biota but also in shaping floodplain commu- nities. Floodplains are rare in naturally constricted Table 2 Water and sediment delivery from large river basins of the world River Drainage area (106 km2 ) Discharge (km3 year1 ) Water yield (mm year1 ) Sediment load (106 t year1 ) Sediment yield (t km 2 year1 ) Amazon 6.15 6300 1024 1200 195 Colorado 0.64 20 31 0.01 0.02 Columbia 0.67 251 375 10 15 Congo (Zaire) 3.72 1250 336 43 12 Danube 0.81 206 254 67 83 GangesBrahmaputra 1.48 971 656 1060 716 Huang He (Yellow) 0.75 49 65 1050 1400 Indus 0.97 238 245 59 61 Mackenzie 1.81 306 169 42 23 Mekong 0.79 470 595 160 202 Mississippi 3.27 580 177 210 64 Niger 1.21 192 159 40 33 Nile 3.03 30 10 0 0 Orinoco 0.99 1100 1111 150 152 St. Lawrence 1.03 447 434 4 4 Source: Milliman JD and Meade RH (1983) Worldwide delivery of river sediment to the oceans. Journal of Geology 91: 121. Table 1 Distinguishing characteristics of rivers, estuaries, and lakes Rivers Estuaries Lakes Water movement Unidirectional, horizontal Bidirectional, horizontal Vertical Water forces Gravitational Tidal Wind-induced Water-level fluctuations Large (seasonal) Variable (daily, storm events) Small (seasonal) Water residence time Daysweeks Weeksmonths Monthsyears Water sources Runoff Runoff, marine, precipitation Runoff, ground water, precipitation Stratification Rare Common (salinity) Common (thermal) Transparency Low (nonalgal particulates) Variable (particulates, dissolved color) High (algae, dissolved color) 144 Hydrology _ Rivers rivers; or may be disconnected if lateral water regula- tion structures (i.e., levees) are present. In constricted and levied channels, the effects of runoff on river velocity and stage are accentuated because the ratio of water volume to bottom area increases with rising stage. Thus, the influence of frictional resistance in dissipating energy is lessened with rising stage. Hydrodynamics of river channels are often depicted using simulation models that describe water move- ments in one, two, or three dimensions (longitudinal, lateral, vertical). These models typically rely on input data describing channel geomorphometry (cross- sectional depictions of river bed and bank elevation) and calibrated using measured surface water eleva- tion and discharge. The models predict surface water elevation under various discharge scenarios and are used to forecast the timing, severity and location of flood events. Water Movement Energy is required to move water and in the case of rivers, this energy is derived from gravitational forces acting along an elevation gradient. Rivers are similar to estuaries in that both are flow-dominated (advec- tive) systems; in estuaries, however, the movement of water is bidirectional and driven by tidal forces (Table 1). Water movement in lakes is driven by comparatively weak forces associated with wind- induced vertical mixing. The slope of the channel and the frictional resistance imposed by its bound- aries determine the velocity with which water is car- ried down the elevation gradient. The roughness of the channel reflects the composition of bed and bank materials and the presence of natural and artificial structures (e.g., woody debris, wing dams). Turbu- lence arises as force is dissipated by frictional resis- tance. This mixing energy maintains particulate matter in suspension and is sufficient to overcome differential heating of surface and bottom layers. Consequently, thermal stratification is rarely observed in rivers except in cases where impoundments are present. The length of time that water resides within a given segment of the river determines in part the potential for physical, chemical, and biological processes to act upon the dissolved and particulate constituents in through-flowing water. Because of the unidirectional 0 50 100 150 200 Precipitation(mm/month) 0 50 100 150 200 J F M A M J J A S O N D Precipitation(mm/month) 0 2000 4000 6000 8000 10000 12000 Discharge(MLd-1) 0 50000 100000 150000 200000 250000 300000 Discharge(MLd-1) Avon river (AU) J- 97 A- 97 J- 97 O- 97 J- 98 A- 98 J- 98 O- 98 J- 99 A- 99 J- 99 O- 99 Kentucky river (USA) Figure 1 The hydrologic regimes of tropical and temperate rivers reflect differences in seasonal patterns of precipitation and evapotranspiration. The Avon River (Western Australia) experiences high evapotransipration throughout the year and variation in discharge is largely driven by seasonal patterns in rainfall. The Kentucky River (North America) receives similar rainfall throughout the year but variation in evapotranspiration results in similar seasonal patterns in river discharge (offset in northern vs. southern hemispheres). Hydrology _ Rivers 145 flow of water, transit time is a useful metric to char- acterize inter-river differences in the time required for water and materials to travel through a reach of specified length. Tracers such as dyes (rhodamine) or conservative solutes (chloride, bromide) are used to measure transit time by tracking the movement of labeled parcels of water. Tracer additions provide a reach-scale estimate that integrates longitudinal, lateral, and depth variations in water velocity. Appli- cation of this technique to larger rivers is problem- atic owing to the quantities of tracer required and the difficulty of achieving a laterally uniform addi- tion. Transit time estimates may be obtained from hydrologic models using measured discharge and cross-sectional area to infer average (cross-sectional) velocity at multiple points along the channel. The coupling of transit time and nutrient uptake, termed nutrient spiraling (glossary), is a concept that has been widely used as a framework for understanding the inter- action between hydrologic and biological processes in regulating nutrient retention. Transit time estimates are also used to design sampling programs in which a parcel of water is sampled repeatedly as it travels down the channel (termed LaGrangian sampling). Geomorphology At any point along a river course, channel morphol- ogy reflects the interplay between the force of water and the stability of bed and bank materials. Channel form is a quasi-equilibrium condition maintained by the dominant discharge and determined in part by the supply of sediment from upstream. Where rivers are not constrained by natural landforms or Floodplain Floodplain river Floodplain river with levies Constricted river Active channel Levies Figure 2 Cross-sectional morphologies of floodplain and constricted rivers. In floodplain rivers, rising river stage results in lateral inundation unless precluded by the presence of levees. Widening of the river during flood events increases frictional forces and reduces water velocity. In constricted rivers, lateral inundation is constrained by steep adjoining slopes resulting in rapidly increasing water velocity with rising river stage. (Illustration by Christopher OBrion, VCU Design Services). 146 Hydrology _ Rivers water regulation structures, channels migrate later- ally (meander) through erosion and redeposition of bank materials. Active channels are characterized by the ephemeral nature of their features (movement of bars and banks) and by their morphological complex- ity, which may include the presence of pools, riffles, side channels, and meanders (Figure 3). Constrained channels occur where natural landforms or water regulation structures limit lateral mobility. High dis- charge results in the erosion of bed materials leading to incised (entrenched) channels of low structural complexity and relatively uniform flow conditions. Channel forms and substrate conditions influence the structure and functioning of riverine food webs. For example, where flow conditions favor the deposition of fine materials, the accumulation of par- ticulate organic matter enhances benthic microbial activity. Various schemes have been devised to cate- gorize channel forms, though these efforts are often confounded by the continuous rather than discrete variation in channel features (e.g., widthdepth ratio; size distribution of bed materials). Emerging technologies for sensing underwater environments hold much promise for linking biological and geo- physical properties particularly in large rivers. Water Regulation Human activities have substantially affected the nat- ural hydrologic cycles of rivers throughout the world. Land-use changes have indirect effects on river hydrology by altering the timing and quantity of run- off from the catchment. For example, urbanization creates impermeable surfaces that increase the vol- ume and speed of storm runoff. Direct impacts include the abstraction (withdrawal) of river water for domestic supply and irrigation as well as the alteration of river channels by water regulation struc- tures. Rivers have been altered through the construc- tion of dams, levees and other channel modifications to accommodate local needs for flood protection, hydropower generation and navigation. Channeliza- tion (straightening) of river courses facilitates naviga- tion but reduces channel and flow complexity thereby diminishing habitat diversity. Channelized rivers are subject to elevated flow velocities that cause erosion and necessitate bank stabilization. Levees preclude lateral exchange and thereby diminish the role of floodplains in material and energy cycles. In flood- prone rivers, biota are adapted to annual flood pulses that provide access to food and spawning areas within the floodplain. Among the most widespread of human impacts on rivers is the construction of dams, which currently number in excess of 45 000 worldwide. Together, their cumulative storage capac- ity is equivalent to 15% of global annual river run- off. Over half of the worlds major rivers are affected by dams, most of which were constructed in the twentieth century. Dams induce pelagic conditions by increasing water storage and dissipating mixing energy. Pelagic conditions favor sediment deposition and biotic assemblages that differ from those occur- ring in flowing environments. The severity of water regulation effects varies according to the number and size of regulation structures along the river course. The cumulative effect of dams within a river basin can be gauged from their number and storage capacity expressed relative to river discharge (Table 3). Low dams (height < 10 m) are designed to maintain a min- imum depth for navigation during low discharge and Figure 3 Selective loss of fine materials may over time create channel reaches that are characterized by a predominance of large substrates such as the gravel bars illustrated here. Their presence in the river channel is important to the maintenance of biodiversity as some species colonize hard substrates or exploit interstitial spaces as a means of adapting to flowing environments. Gravel bars and other subsurface exchange zones are also important to ecosystem function such as nutrient retention. Photo of the Rio Apurimac in Peru by A. Aufdenkampe (see related paper by Aufdenkampe et al. (2007) Organic Geochemistry 38: 337). Hydrology _ Rivers 147 thereby regulate stage but do not eliminate flowing conditions. High dams are designed for flood control and water storage. They inundate large areas and effectively create lake-like conditions, in some cases, resulting in thermal stratification of the water column. Water Quality Rivers integrate drainage waters from distant points in the landscape that may differ in topography, soils, vegetation, and land use. These differences give rise to widely varying water chemistry within river basins particularly where anthropogenic influences differ among sub-basins. Along the river course, water chemistry changes in response to inputs from these diverse sources and also reflects variable water resi- dence times in channel, hyporheic, and lateral storage zones. Particulate Matter High concentrations of suspended particulate matter are a characteristic feature of rivers particularly during periods of elevated discharge. The upward component of water turbulence acts to maintain par- ticulate matter in suspension, resulting in down- stream transport. Particulate matter may originate within the channel through erosion of bed and bank materials, resuspension of sedimented materials, and biological production. Most particulate matter, how- ever, is derived from sources outside the river channel that are transported via tributary streams. The rivers of Asia are particularly noted for their high sediment load. It is estimated that the Ganges, Brahmaputra, and Yellow Rivers contribute 20% of the total sedi- ment load transported to the oceans (Table 2). High sediment production is attributed to natural factors affecting surface erosion (soil composition, steep slopes, and intensive rainfall) as well as anthropo- genic effects associated with deforestation and urban- ization. Riverine suspended matter is predominantly a fine-grained (2830 l s1 ) 2nd magnitude (2832830 l s1 ) 3rd magnitude (28.3283 l s1 ) 4th magnitude (6.328.3l s1 ) 5th magnitude (0.636.3l s1 ) 6th magnitude (63630ml s1 ) 7th magnitude (863 ml s1 ) 8th magnitude ( 100%) Subvariable (n 25100%) Constant (n < 25%)a 21, 26 Impermanent (1000 years) 9 Continuous Steady (perennial: base flow) Variable (perennial) Periodic (rhythmic or episodic) Discontinuous (intermittent) Nonexistent (paleo- or abandoned spring) 1, 35 Water chemistry pH and hardness Acidic, soft water Alkaline, hard water 16 Total dissolved solids Freshwater springs (35 000 mg l1 ) 9, 39 Principal ions Chloride spring water Sulfate spring water Sulfatechloride spring water Carbonate (tufaceous) spring water Sulfatecarbonate spring water Chloridecarbonate spring water Chloridesulfatecarbonate spring water Siliceous spring water Borate spring water Nitrate spring water Phosphate spring water Chalybeate (iron hydroxide) spring water Acid spring water 6, 35 Continued Hydrology _ Springs 159 Table 1 Continued Classification type Categories (examples) Sources Oxygen level Aerobic (high oxygen) Anaerobic (low oxygen) 25 Water temperature Temperature with respect to MAAT of a region, and human body temperature Cold springs (water cooler than MAAT) Ambient springs (water temperature approximates MAAT) Superambient (thermal or geothermal) springs (water warmer than MAAT)b Hot springs (water warmer than human body temperature % 3738 C or 98100 F) 28, 29 Nonthermal cold springs (water temperature < MAAT) Warm springs (water temperature > MAAT, but 98 F) 23 Absolute temperature range Cold springs (50 C) 38 Cold springs (40 C) 9 Cold (40 C) 27 Cold or hypothermic (70 C) 42 Variation and magnitude of temperature Heterothermal springs with varying temperatures Homothermal springs with same temperatures year-round Cold springs (water cooler than or at annual mean temperature of place) Tepid springs (water warmer than annual mean temperature, but cooler than mean maximum temperature of place) Hot springs (water warmer than mean maximum temperature of place) Relatively hot springs (springs without a special animal and plant community; temperature between mean maximum temperature of place and 40 C) Absolutely hot springs (springs with a special animal and plant community, or no life at all, excepting bacteria; temperature >40 C). 37 Relation to fauna and flora Hypothermophilous formations (4.416 l s1 ) 26 Based on purpose Air-conditioning, bottling, brewing and distilling, commercial, domestic, industrial, institutional, irrigation, mining, religious, sightseeing, public supply, recreation, stock supply, fish culture, etc. 19, 35 a Variability index (n) [(m l)/a] 100, where m maximum flow, l minimum flow, and a mean flow. b Some researchers propose that a spring should not be considered thermal unless it exceeds the MAAT by a certain amount (e.g., by 510 C: see source 39). c Based on authors rough translation from the original German. 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Michaelis FB (1976) Physico-chemical features of Pupu Springs. New Zealand Journal of Marine and Freshwater Research 10: 613628. 23. Meinzer OE (1927) Large springs in the United States. United States Geological Survey Water-Supply Paper 557: 194. 24. Nesterovich A (1996) Studies of the fauna of Belarusian springs. Crunoecia 5: 7985. 25. Odum HT (1957) Primary production estimates in eleven Florida springs and a marine turtle grass community. Limnology and Oceanography 2: 8597. 26. Otton EG and Hilleary JT (1985) Maryland Springs Their Physical, Thermal, and Chemical Characteristics. Baltimore: Maryland Geological Survey Report of Investigations 42. 27. Parish LC and Lott TM (eds.) (1996) Balneology and the spa: the use of water in dermatology. Clinics in Dermatology 14: 547692. 28. Pentecost A (2005) Hot springs, thermal springs and warm springs. Whats the difference? Geology Today 21: 222224. 29. Pentecost A, Jones B, and Renault RW (2003) What is a hot spring? Canadian Journal of Earth Sciences 40: 14431446. 30. Pe rez ES (1996) Springs in Spain: classification according to their flows and lithologies and their hydraulic contributions. Ground Water 34: 10331041. 31. Sada DW and Pohlmann KF (2003) U.S. National Park Service Mojave Inventory and Monitoring Network Spring Survey Protocols: Level I (http://www. 32. Sada DW, Williams JE, Silvey JC, Halford A, Ramakka J, Summers P, and Lewis L (2001) Riparian area management: a guide to managing, restoring, and conserving springs in the western United States. Technical Reference 173717. Denver, Colorado: United States Department of the Interior Bureau of Land Management. 33. Scott TM et al. (2004) Springs of Florida. Florida Geological Survey Bulletin 66: 1658. 34. Shuster ET and White WB (1971) Seasonal fluctuations in the chemistry of limestone springs: A possible means for characterizing carbonate aquifers. Journal of Hydrology 14: 93128. 35. Smart C and Worthington RH (2004) Springs. In: Gunn J (ed.) Encyclopedia of Caves and Karst Science, pp. 699703. New York: Taylor and Francis. 36. Thienemann A (1922) Hydrobiologische untersuchungen an quellen. Archiv fur Hydrobiologie 14: 151190. 37. Tuxen SL (1944) The hot springs of Iceland: Their animal communities and their zoogeographical significance. In: Frioriksson A, et al. (eds.) The Zoology of Iceland, vol. I, part II, pp. 1206. Copenhagen: Ejnar Munksgaard. 38. United States NOAA Geophysical Data Center. 39. van Everdingen RO (1991) Physical, chemical, and distributional aspects of Canadian springs. Memoirs of the Entomological Society of Canada 155: 728. 40. Verdonschot PFM (1996) Towards ecological spring management. Crunoecia 5: 183194. 41. Verdonschot PFM and Schot JA (1986) Macrofaunal community types in helocrene springs. Report of Research Institute of Nature Management 1986/ 1987: 85103. 42. Vouk V (1923) Die probleme der biologie der thermen. Internationale Revue der Gesamten Hydrobiologie und Hydrographie 11: 8999. 43. White WB (1988) Geomorphology and Hydrology of Karst Terrains. New York: Oxford University Press. 44. Wolejko L (1996) Transformation of spring-mire vegetation in north-western Poland in relation to human impact. Crunoecia 5: 5966. 45. Worthington SRH (1991) Karst hydrogeology of the Canadian Rocky Mountains. Hamilton, ON: McMaster University Dissertation. 46. Zollho fer JM, Brunke M, and Gonser T (2000) The typology of springs in Switzerland by integrating habitat variables and fauna. Archiv fur Hydrobiologie Supplementband Monographic Studies 121: 349376. 162 Hydrology _ Springs population density data are available, and an amphi- pod or isopod crustacean is the most abundant in 62% (Table 2). In addition, spring-like faunal assem- blages dominated by amphipods, isopods, and (or) mollusks occur in the flow- and temperature-constant tailwaters of many reservoir deep-release dams. Various factors hypothetically contributing to the dominance of noninsect macroinvertebrates in non- thermal, hard-water springs are depicted as a flow- diagram (Figure 6). The abundance and (or) diversity of macroinverte- brates is often higher in perennially flowing springs than in intermittent springs. Large springs also tend to have more species than do smaller springs. Macro- invertebrate abundance, diversity, and microhabitat dis- tribution may be influenced by substrate type and macrophyte density, as well. Macrophytes, such as watercress (Nasturtium spp.) which is characteristic of temperate hard-water springs worldwide, enhance macroinvertebrate abundance by supplying refuges from water currents and fish predation, and by trapping large amounts of detrital food particles. Amphipods, isopods, and other macroinvertebrates may also reach especiallyhighdensitiesinspringswheretherearenofish predators. In addition, many lotic species live in rheo- crenes, whereas many lentic species inhabit limnocrenes. Often the species diversity of macroinvertebrates increases from ground waters to surface spring habi- tats to downstream sites. This longitudinal pattern 2.0 y=1.22(X) 1.93 r=0.62; P=0.002 0 1 2 3 2.5 3.0 Log10 maximum relief (m) Log10numberofthermalsprings per1000000km2 3.5 4.0 Figure 4 Log10 density of thermal springs in each of 50 states of the United States in relation to topographic relief (the log10 maximum range in elevation in a county). The positively significant regression line and equation (along with r, the correlation coefficient, and P, the probability that this relationship is due to chance) are depicted for 22 states (solid circles) that have recorded thermal springs. Alaska (star) was not included in this regression because it was considered an outlier. For comparison, the other 27 states with no thermal springs are plotted as 0 (arithmetic) values (open circles). Note that only 25% of the 36 states with a maximum relief less than 6000 m have thermal springs, whereas all of the 14 states with greater maximum relief have thermal springs. Data are from the United States National Geophysical Data Center (http://www.ngdc.noaa. giv/nndc/struts/describeField?t100006&s1&field11029) and Maximum Relief Counties by State compiled by J. Brekhus ( counties.html). 7 15 3 Limestone/dolomiteOtherbedrock 0 20 40 60 80 100 Percentageofspringsystems dominatedbynoninsecttaxa Low altitude (500m) 0 20 40 60 80 100 11 Figure 5 Percentage of spring systems (bars) in North America, Europe, and New Zealand numerically dominated by noninsect macroinvertebrates in relation to altitude and geology (number of springs above each bar). Note that noninsect dominance is most frequent in low altitude spring systems with calcium-rich bedrock, whereas insect dominance is most frequent in high altitude spring systems underlain by other kinds of bedrock. Data (with minor modification) from Barqun J and Death RG (2006) Spatial patterns of macroinvertebrate diversity in New Zealand springbrooks and rhithral streams. Journal of the North American Benthological Society 25: 768786. Hydrology _ Springs 163 Table 2 Population density of the most abundant macroinvertebrate species in each of several nonthermal spring systems in Europe and North America Country (state or province) Spring Most abundant species Mean population density (number m2 ) Source Canada (Ontario) Valley Nemoura trispinosa (P) 11 604 17 Denmark Ravnkilde Nemourella picteti (P) 16 561 6 Rold Kilde Gammarus pulex (A) 2320 5 Spain Springs 16 Echinogammarus sp. (A)a 1028 1 Switzerland Q1 Gammarus fossarum (A) 1850 15 Q2 G. fossarum (A)b 600 15 Q3 G. fossarum (A) 275 15 Q4 G. fossarum (A) 1575 15 Q5 G. fossarum (A) 1950 15 Q6 Pisidium spp. (B)b 1300 15 Q7 G. fossarum (A) 450 15 Q8 G. fossarum (A) 5567 15 Q9 Pisidium spp. (B) 3275 15 Q10 G. fossarum (A) 3400 15 United Kingdom Cowdale Nemoura erratica (P) 385 10 Kidtor Gammarus pulex (A) 3583 10 Ashwood Dale G. pulex (A)b 400 10 Woolow G. pulex (A)c 945 10 Topley Pike G. pulex (A) 2273 10 Wormhill, W Nemurella picteti (P) 4188 10 Wormhill, E N. picteti (P) 2355 10 Cheedale, W G. pulex (A) 875 10 Cheedale, E G. pulex (A)d 123 10 Cheedale Bridge G. pulex (A) 1430 10 Litton Mill G. pulex (A)b 25 10 White Cliff G. pulex (A) 1818 10 Lees Bottom 1 G. pulex (A)e 1135 10 Lees Bottom 2 G. pulex (A) 950 10 Lower Dimindale 1 G. pulex (A) 793 10 Lower Dimindale 2 G. pulex (A) 1985 10 Great Shacklow 1 G. pulex (A)c 303 10 Great Shacklow 2 G. pulex (A) 2560 10 United States (California) Jamesf Gumaga nigricula (T) 1694 9 (Idaho) Paris Acrynopteryx signata (P) 1520 14 (Iowa) Cone Pentaneura sp. (D) 504 13 (Kentucky) Morgans Gammarus minus (A) 234 7 (Massachusetts) Rootg Limnodrilus hoffmeisteri (O) 5465 12 (New Mexico) Lander Gammarus desperatus (fasciatus) (A) 10 416 8 (Ohio) OZ Lirceus fontinalis (I) 46 2 (Pennsylvania) Ell Fontigens nickliniana (G) 17 601 4 (Tennessee) Root Stictochironomus sp. (D) 8110 16 Unnamed Caecidotea intermedius (Asellus militaris) (I)b 178 11 (Utah) Big Paludestrina sp. (G) 1620 14 Cascade Hyalella azteca (A) 15 172 14 China Row Baetis tricaudatus (E) 344 14 Clover Creek H. azteca (A) 26 916 14 Conrad Paludestrina sp. (G) 13 286 14 Ricks B. bicaudatus (E) 586 14 Thousand Paludestrina sp. (G) 843 14 (Washington) Tyee Planorbis sp. (G)b 1424 3 The water in these systems is perennially flowing and has approximately neutral pH and is enriched with calcium and bicarbonate ions, except where noted. A Amphipoda; B Bivalvia; D Diptera; E Ephemeroptera; G Gastropoda; I Isopoda; O Oligochaeta; P Plecoptera; T Trichoptera. a Mean population density in six springs. b Not counting the more abundant Chironomidae, which were not distinguished at the species level. c Not counting the more abundant Oligochaeta, which were not distinguished at the species level. d Not counting the more abundant Psychodidae, which were not distinguished at the species level. e Not counting the more abundant Simuliidae, which were not distinguished at the species level. 164 Hydrology _ Springs has been related to an increase in temperature fluc- tuations downstream, as well as to other factors, but is still not well understood. Nevertheless, macroinver- tebrates can be very diverse in springs with heteroge- neous substrates and microhabitats. In addition, in some springs (as in New Zealand) macroinvertebrate species diversity decreases with distance from the spring source. Furthermore, macroinvertebrate abun- dance (number of individuals) is often as high or higher in springs than at downstream sites or nearby runoff streams. The abundance and diversity of other kinds of spring-dwelling organisms, such as algae, macro- phytes, microinvertebrates, and vertebrates, may also be influenced by food availability, light conditions, substrate type, human influences, and (or) water tem- perature, chemistry, and flow rate. However, unlike the typical pattern seen for macroinvertebrates, diatoms appear to decrease in diversity from spring heads to downstream sites with faster flow rates. The inhabitants of springs include species largely restricted to these habitats (crenobionts), species that commonly occur in spring habitats, but also occur elsewhere (crenophiles), species that are found in a variety of aquatic habitats and only occasionally occur in springs (crenoxenes), and subterranean spe- cies that have been washed into spring habitats from ground waters. Some crenobionts are so specialized for life in springs that this is reflected in their scientific name: e.g., the flatworm Crenobia alpina in Europe, midges of the genera Krenopelopia, Krenopsectra, and Krenosmittia in the Holarctic region, snails of the genus Fontigens, the fountain darter Etheostoma fonticola, and springfish of the genus Crenichthys in North America, the water mite Torrenticola fontinale in Costa Rica, and isopods of the genus Crenoicus in Australia, to name a few. The kingdom Crenarch- aeota was even given its name because the first species discovered in this group of single-celled archaea were found in hot springs (see next section). The relative proportion of crenobionts in a spring depends on habitat type, persistence, isolation, and level of dis- turbance. Thermally constant springs in temperate regions have provided refuges for relict species (such as C. alpina) that have survived the great climatic shifts of the Pleistocene. In arid areas, relatively isolated, perennially flowing springs and their asso- ciated riparian habitats are also havens for rare or endemic animals and plants. Thermal Springs The hottest thermal springs with water temperatures exceeding 70 C are exclusively populated by viruses, archaea, and bacteria (Table 3). Some archaea, which are low-energy microbes especially well adapted to extreme environmental conditions, can even live and grow in springs with boiling (temperatures >100 C), highly acidic (pH < 2), or highly alkaline (pH > 9) water. Archaea are very diverse in hot springs and include types near the evolutionary root of all life. Viruses are also remarkably diverse featuring a variety f Water ceases flowing during droughts. g Water mildly acidic (pH 5.56.0). Sources 1. Barqun J and Death RG (2004) Patterns of invertebrate diversity in streams and freshwater springs in northern Spain. Archiv fur Hydrobiologie 161: 329349. 2. Butler MJ and Hobbs HH (1982) Drift and upstream movement of invertebrates in a springbrook community ecosystem. Hydrobiologia 89: 153159. 3. Davidson FA and Wilding JL (1943) A quantitative faunal investigation of a cold spring community. American Midland Naturalist 29: 200209. 4. Gooch JL and Glazier DS (1991) Temporal and spatial patterns in mid-Appalachian springs. Memoirs of the Entomological Society of Canada 155: 2949. 5. Iversen TM (1988) Secondary production and trophic relationships in a spring invertebrate community. Limnology and Oceanography 33: 582592. 6. Lindegaard C, Thorup J, and Bahn M (1975) The invertebrate fauna of the moss carpet in the Danish spring Ravnkilde and its seasonal, vertical, and horizontal distribution. Archiv fur Hydrobiologie 75: 109139. 7. Minshall GW (1967) Role of allochthonous detritus in the trophic structure of a woodland springbrook community. Ecology 48: 139149. 8. Noel MS (1954) Animal ecology of a New Mexico springbrook. Hydrobiologia 6: 120135. 9. Resh VH (1983) Spatial differences in the distribution of benthic macroinvertebrates along a springbrook. Aquatic Insects 5: 193200. 10. Smith H, Wood P, and Gunn J (2001) The macroinvertebrate communities of limestone springs in the Wye Valley, Derbyshire Peak District, UK. Cave and Karst Science 28: 6778. 11. Stern MS and Stern DH (1969) A limnological study of a Tennessee cold springbrook. American Midland Naturalist 82: 6282. 12. Teal JM (1957) Community metabolism in a temperate cold spring. Ecological Monographs 27: 283302. 13. Tilly LJ (1968) The structure and dynamics of Cone Spring. Ecological Monographs 38: 169197. 14. Van Gundy JJ (1973) Factors Controlling the Diversity and Abundance of Macroinvertebrates in Non-thermal Springs. Dissertation. Salt Lake City, University of Utah. 15. von Fumetti S, Nagel P, and Baltes B (2007) Where a springhead becomes a springbrook A regional zonation of springs. Fundamental and Applied Limnology 169: 3748. 16. Wilhm JL (1970) Some aspects of structure and function of benthic macroinvertebrate populations in a spring. American Midland Naturalist 84: 2035. 17. Williams DD and Hogg ID (1988) The ecology and production of invertebrates in a Canadian coldwater spring-springbrook system. Holarctic Ecology 11: 4154. Hydrology _ Springs 165 of shapes including rods, spindles, filaments, droplets, spheres, polyhedrons, and forms resembling bottles and two-tailed lemons. They also have unique genes that are unknown elsewhere in the biosphere. More- over, they provide insight into the common ancestry of viruses infecting species in all three of the domains of life (Archaea, Bacteria, and Eukarya). Many kinds of bacteria with diverse biochemical mechanisms for harnessing energy abound in hot springs, as well. Some are autotrophic, producing their own food by using light energy (photosynthesis) or chemical energy from inorganic materials (chemo- synthesis), whereas others are heterotrophic, using the fermentation products of the autotrophs. These microbial communities can be quite complex and often consist of extensive, visible mats dominated by filamentous cyanobacteria, other photosynthetic bac- teria, and eukaryotic algae. However, photosynthetic organisms only occur at temperatures below 73 C (Table 3). Relatively few multicellular plants and animals live in hot springs because they cannot toler- ate temperatures above $5060 C (Table 3). Ani- mal, algal, and fungal diversities decrease as spring temperature increases (Figures 7 and 8). Longitudinal zonation of photosynthetic microbes is apparent in many thermal streams, with cyanobacteria dominat- ing the spring head, and eukaryotic algae and diatoms being most abundant downstream where it is cooler. Hot springs have attenuated food chains. Most aquatic animals, if present, are herbivores, grazing on the microbial mats. They are mostly insects, such as flies, bugs, beetles, and odonates, but a few species of nematode and annelid worms, rotifers, water mites, mollusks, crustaceans, fish, and amphibians may occur in thermal springs with temperatures between 30 and 55 C. Air-breathing may facilitate survival of some insect larvae in hot springs with relatively low oxygen levels. The most thermophilic animal known is the Increased numbers of peracaridans mollusks, and turbellarians but decreased numbers of insects Non-emergent lifestyle High population densities Intense competition for resources Higher efficiency of resource use More food Increased aquatic vegetation Reduction of downstream losses Bed stability and water clarity Flow constancy Thermal constancy Year-round primary production Year-round reproduction Lack of thermal cues for timing life history events Inter-spring dispersal is difficult Small, isolated habitat area Paucity of large predators Protection of eggs and other vulnerable life stages Figure 6 A hypothetical framework explaining the dominance of noninsect macroinvertebrates (peracaridan crustaceans including amphipods and isopods, mollusks including snails and clams, and turbellarian flatworms) in temperate nonthermal springs. The physical stability, small isolated area and paucity of large predators typical of these springs are considered to be the major environmental factors causing their distinctive macroinvertebrate fauna. Reproduced from Glazier DS (1991) The fauna of North American temperate cold springs: patterns and hypotheses. Freshwater Biology 26: 527542, with permission from Blackwell. 166 Hydrology _ Springs nematode Aphelenchoides sp., which can tolerate tem- peratures up to 61.3 C. However, no vertebrate ani- mal is known to live in spring water with a temperature exceeding 41 C (Table 3). Importance of Springs Springs are important geologically and ecologically, and are of value to humans in several ways. Geological Importance The number of springs is not known for most geo- graphical regions, and those few regional estimates that have been made (calculated here as density or number per area) vary by over three orders of magni- tude (Table 4). However, if one extrapolates from these estimates, there are worldwide on land (not counting Antarctica) probably more than four springs per 10 km2 (global total > 57 000 000) and more than seven thermal springs per 10 000 km2 (global total > 100 000). These numbers are underestimates because they are based on surveys that usually ignore small springs and seeps, which greatly exceed the number of larger springs. For example in Spain, spring size, as estimated as flow volume (l s1 ), is inversely corre- lated with observed spring frequency (Figure 9). Because of their abundance, springs are obviously an important part of the hydrologic cycle, and they are also an important source of erosion and transport of dissolved minerals. In humid karstic areas, spring Table 3 Upper temperature limits of recorded occurrence of various groups of organisms in subaerial (terrestrial) springs Group Upper temperature limit ( C) Prokaryotes Archaea 103 Bacteria 100 Cyanobacteria (blue-green algae) 73a Photosynthetic bacteria 73 Eukaryotes Protists Algae 70 Protozoa 58a Fungi 62 Plants 50 Animals Invertebrates Nematoda 61 Rotifera 46 Acari 51 Crustacea 55 Mollusca 46 Insecta 51 Vertebrates Fishes 40 Amphibia 41 Even higher limits have been found for prokaryotes at the hydrothermal vents of submarine springs. a Some old reports of higher temperature limits have been discounted by Brock (1978). Sources Adams MWW and Kelly RM (1995) Enzymes from microorganisms in extreme environments. Chemical and Engineering News 73: 3242. Brock TD (1978) Thermophilic Microorganisms and Life at High Temperatures. New York: Springer-Verlag. Brock TD (1985) Life at high temperatures. Science 230: 132138. Jana BB, Pal DN, and Sarkar HL (1982) Spatial distribution of the biotic community in the thermal gradients of the two hot springs. Acta Hydrochimica et Hydrobiologica 10: 101108. Kahan D (1969) The fauna of hot springs. Verhandlungen der Internationalen Vereinigung fur Theoretische und Angewandte Limnologie 17: 811816. Kashefi K, Holmes DE, Reysenbach A-L, and Lovley DR (2002) Use of Fe(III) as an electron acceptor to recover previously uncultured hyperthermophiles: Isolation and characterization of Geothermobacterium ferrireducens gen. nov., sp. nov. Applied and Environmental Microbiology 68: 17351742. Kristjansson JK (ed.) (1992) Thermophilic Bacteria. Boca Raton, Florida: CRC Press. Obrdlik P (1988) The Longola Hot Springs of Zambia: The need for conservation. Biological Conservation 43: 8186. Poinar GO (2001) Nematoda and Nematomorpha. In: Thorp JH and Covich AP (eds.) Ecology and Classification of North American Freshwater Invertebrates, 2nd edn., pp. 255295. San Diego: Academic Press. Stetter KO (1998) Hyperthermophiles: Isolation, classification and properties. In Horikoshi K and Grant WD (eds.) Extremophiles: Microbial Life in Extreme Environments, pp. 124. New York: Wiley-Liss. Winterbourn MJ (1968) The faunas of thermal waters in New Zealand. Tuatara 16: 111122. Hydrology _ Springs 167 flow can account for up to one-half of the land ero- sion. In the United States, 3040% of flowing surface waters has been estimated to be from ground water emerging from springs. Some springs also produce chemical and biological deposits that significantly alter the local landscape. Ecological Importance Springs provide many benefits to both aquatic and terrestrial life, including moisture, drinking water, food, minerals, shelter, thermal refuges, breeding sites, and travel corridors. Many kinds of plants and animals use thermally stable springs to endure hot summers or cold winters (e.g., Figure 10). Some springs have very high productivities, near the highest known in natural ecosystems. However, some acidic and sulfu- rous springs may have harmful effects on local ecologi- cal communities, including acidification and leaching of toxic metals that adversely affect downstream life, and production of sulfuric acid that can damage local vegetation. Highly carbonated springs emit CO2 that may have both positive and negative effects on the local biota. Scientific Importance Springs and spring brooks are useful systems for studying a wide variety of scientific problems. Springs are places where interactions between land, water, air, 4 30 0 20 40 60 32 34 36 38 40 42 44 46 514 1520 0 5 10 NumberofspeciesNumberofspecies 15 20 25 Water temperature (C) Animals in Iceland springs Dytiscid beetles in western United States springs 2125 2630 3135 36404145 4650 >50 Figure 7 Number of species in relation to water temperature for dysticid beetles in western United States thermal springs [data from Brues CT (1932) Further studies on the fauna of North American hot springs. Proceedings of the American Academy of Arts and Sciences 67: 185303] and for animals in Iceland springs [data from Tuxen SL (1944) The hot springs of Iceland; their animal communities and their zoogeographical significance. In: Frioriksson A, et al. (eds.) The Zoology of Iceland, volume I, part II, pp. 1206. Copenhagen: Ejnar Munksgaard]. NumberofspeciesNumberofspeciesNumberofspecies 20 0 5 10 15 25 30 35 40 45 50 35 0 5 10 15 20 0 5 10 15 20 25 40 45 50 55 25 30 35 Water temperature (C) 40 45 60 Macroinvertebrates in a California thermal spring stream Algae in a Montana thermal spring stream Fungi and plankton in two India thermal spring streams Fungi Plankton 55 Figure 8 Number of species in relation to water temperature for macroinvertebrates in a California thermal spring stream [data from Lamberti GA and Resh VH (1985) Distribution of benthic algae and macroinvertebrates along a thermal stream gradient. Hydrobiologia 128: 1321], for algae in a Montana thermal spring stream [Jackson Hot Springs; data from Kullberg RG (1971) Algal distribution in six thermal spring effluents. Transactions of American Microscopical Society 90: 412434], and for fungi and plankton in two India thermal spring streams [data from Chandrashekar KR, Sridhar KR, and Kaveriappa KM (1991) Aquatic hyphomycetes of a sulphur spring. Hydrobiologia 218: 151156; and Tanti KD and Saha SK (1993) Hydrobiological profiles along a thermal gradient of the hot springs of Rajgir (Bihar), India. Journal of Freshwater Biology 5: 107117]. 168 Hydrology _ Springs Table 4 Estimated number and density of springs in some different geographical regions of the world Region Number of springs Geographical area (km2 )a Density of springs (per 1000 km2 ) Source Asia China >2500b 9 578 678 >0.26b 12 India >300b 3 287 590 >0.09b 11 Japan Vicinity of Mt. Fuji $180 32 Vicinity of Aso volcano >1500 32 Turkey Anatolia >1800b 755 688 >2.4b 24 Yemen >100b 528 038 >0.19b 16 Australia Great Artesian Basin 3000c 1.8c 20 2000d 1 711 000 1.2d 20 Europe England White Peak area of Peak District 48 540 88.9 31 Finland (central) 25 00030 000 19 700 13001500 22 Germany Berchtesgaden Alps 416 162 2568 6 Gu tersloh District 203 220 923 8 North Rhine-Westphalia $2000 34 069 $59 14 Pfa lzerwald Mountains 141 1770 80 9 Ireland 29b 70 284 0.4b 1 Italy (central) 147b $100 000 1.5b 15 Netherlands Northern part of province of Limburg 47 4 Portugal (northern) >1500 650 >2300 18 Slovenia 28b 20 151 1.4b 22 Spain (62% of area) 17 305 342 428 50.5 19 Sweden Province of Go teborg & Bohus $100 5141 $20 13 New Zealand South Island flood plains of three rivers 165 656.5 251.3 7 North America Mexico Yucata n >3000 38 402 >78.1 33 United States 1661b 9 161 770 0.18b 27 Florida >700 139 670 >5.0 5 Illinois >200 144 120 >1.4 30 Kansas Thousands 3 Missouri >3000 178 414 >16.8 17 Nevada Spring Mountains $300 $4000 $75 21 New Mexico Oscura and San Andres Mountains 276 $3500 $79 28 Texas $2000e 2 Utah $10 000 212 752 $50 29 Virginia >1500 105 586 >14.2 10 100b 0.9b 10 South America Argentina Jujuy $40b 53 219 $0.75b 26 Chile >240b 748 800 >0.32b 25 a Some areas are total areas; others are land area only. b Thermal springs only c Estimated number and density of springs before 1870. d Estimated number and density of springs at present e For only 183 of 254 counties in state Sources 1. Beckett B, Tiorney A, and Emblow C (2003) Irish thermal springs ( 2. Brune G (2002) Springs of Texas, vol. I. College Station: Texas A & M University Press. 3. Buchanan R, Sawin R, and Lebsack W (2000) Water of the most excellent kind: historic springs in Kansas. Kansas History 23: 128144. Hydrology _ Springs 169 and life are brought into sharp focus. Ground water interacts chemically and physically with subsurface rocks while traveling underground and then interacts with air and various organisms when it emerges above ground. As a result, several important geologi- cal phenomena can be investigated in spring systems, including subsurface hydrogeology, mineral deposi- tion, geomicrobiology, and geothermal processes. In addition, the sediments deposited at springs enable past climatic and hydrogeological conditions of local regions to be estimated. And the chemical composi- tion of spring water can provide clues to groundwater temperatures. Spring systems are also wonderful natural labora- tories for biologists and environmental scientists. The nearly constant water temperature, flow rate, and chemistry of many springs allow many biological processes to be studied under naturally controlled con- ditions that can also be relatively easily duplicated in the laboratory. Furthermore, springs differ significantly in many ways, even in local regions e.g., in size, isolation, water temperature, flow rate, chemistry, sub- strate, and other ecological characteristics thus providing excellent opportunities for comparative work. Since springs are often numerous in many places, they may supply natural replicates of various environmental conditions, thus also enabling useful field experiments to be carried out. The stable conditions within springs, combined with significantly different conditions among springs, 4. Fellinger M and Verdonshot P (1996) In search of springs in the northern part of the province Limburg (the Netherlands). Crunoecia 5: 287288. 5. Florida springs, Florida Department of Environmental Protection ( 6. Gerecke R, Meisch C, Stoch F, Acri F, and Franz H (1998) Eucrenonhypocrenon ecotone and spring typology in the Alps of Berchtesgaden (Upper Bavaria, Germany): A study of Microcrustacea (Crustacea: Copepoda, Ostracoda) and water mites (Acari: Halacaridae, Hydrachnellae). In: Botosaneanu L (ed.) Studies in Crenobiology: The Biology of Springs and Springbrooks, pp. 167182. Leiden: Backhuys. 7. Gray DP (2005) Braided River Springs: Distribution, Benthic Ecology and Role in the Landscape. Canterbury, New Zealand: University of Canterbury Dissertation. 8. Gro ver W (1996) Erfahrungen mit der umsetzung des quellschutzkonzeptes im Kreis Gu tersloh. Crunoecia 5: 161166. 9. Hahn HJ (2000) Studies on classifying of undisturbed springs in southwestern Germany by macrobenthic communities. Limnologica 30: 247259. 10. Helfrich LA, Parkhurst J, and Neves R (2005) Managing Spring Wetlands for Fish and Wildlife Habitat. Virginia Cooperative Extension Publication 420537. Blacksburg: Virginia Polytechnic Institute and State University. 11. Jana BB (1973) The thermal springs in Bakreswar, India: Physico-chemical conditions, flora and fauna. Hydrobiologia 41: 291307. 12. Keshi A (1980) Thermal springs in China. GeoJournal 4.6: 507513. 13. La ng L-O and Swedberg S (1995) Selection of springs for the groundwater monitoring program of the province of Go teborg and Bohus, SW Sweden. Water, Air and Soil Pollution 85: 18371842. 14. Lauko tter G (1996) Vom AK quellschutz zur quellschutzkampagne NRW. Crunoecia 5: 103108. 15. Minissale A (2004) Origin, transport and discharge of CO2 in central Italy. Earth-Science Reviews 66: 89141. 16. Minissale A, et al. (2007) Thermal springs, fumaroles and gas vents of continental Yemen: their relation with active tectonics, regional hydrology and the countrys geothermal potential. Applied Geochemistry 22: 799820. 17. Missouri Department of Natural Resources ( 18. Pacheco FAL and Alencoa o AMP (2002) Occurrence of springs in massifs of crystalline rocks, northern Portugal. Hydrogeology Journal 10: 239253. 19. Pe rez ES (1996) Springs in Spain: Classification according to their flows and lithologies and their hydraulic contributions. Ground Water 34: 10331041. 20. Ponder WF (2002) Desert springs of the Australian Great Artesian Basin. Conference Proceedings. Spring-fed wetlands: Important scientific and cultural resources of the intermountain region ( 21. Sada DW, Fleishman E, and Murphy DD (2005) Associations among spring-dependent aquatic assemblages and environmental and land use gradients in a Mojave Desert mountain range. Diversity and Distributions 11: 9199. 22. S ajna N, Haler M, S kornik S, and Kaligaric M (2007) Survival and expansion of Pistia stratiotes L. in a thermal stream in Slovenia. Aquatic Botany 87: 7579. 23. Sa rkka J, Levonen L, and Ma kela J (1998) Harpacticoid and cyclopoid fauna of groundwater and springs in southern Finland. Journal of Marine Systems 15: 155161. 24. Sayili M, Akca H, Duman T, and Esengun K (2007) Psoriasis treatment via doctor fishes as part of health tourism: A case study of Kangal Fish Spring, Turkey. Tourism Management 28: 625629. 25. Spas and hot springs in Chile ( 26. Thermal springs in Jujuy, Argentina ( 27. Thermal springs list for the United States, United States National Geophysical Data Center ( t=100006&s=1&filed=11029) 28. Thompson BC, Matusik-Rowan PL, and Boykin KG (2002) Prioritizing conservation potential of arid-land montane natural springs and associated riparian areas. Journal of Arid Environments 50: 527547. 29. Utah Water Research Laboratory ( 30. Webb DW, Wetzel MJ, Reed PC, Philippe LR, and Harris MA (1995) Aquatic biodiversity in Illinois springs. Journal of the Kansas Entomological Society 68 (Supplement): 93107. 31. Wood PJ, Gunn J, Smith H, and Abas-Kutty A (2005) Flow permanence and macroinvertebrate community diversity within groundwater dominated headwater streams and springs. Hydrobiologia 545: 5564. 32. Yamamoto S. Springs of Japan. Environmental Geology 27: 118119. 33. Yucatan today the tourist guide ( 170 Hydrology _ Springs are especially useful for incisive analyses of the in situ effects of various environmental factors on the temporal dynamics of biological systems at several hierarchical levels from single organisms to whole biotic communities. Unfortunately, however, these valuable research opportunities have not been suffi- ciently exploited. As one heuristic example, consider how a simple comparative analysis of springs with different mean water temperatures reveals novel pat- terns of how temperature affects rates of community- level production. At each trophic level of a spring community, production appears to increase and then decrease as temperature increases, with peak prod- uctivities occurring near 39 C for producers, 23 C for primary consumers, and 13 C for secondary con- sumers (Figure 11). These previously unreported pat- terns require further study and verification before they can be fully understood, but presumably they are partly the result of increasing temperature increasing the rates of biosynthetic chemical reactions up to a point beyond which higher temperatures cause deleterious metabolic costs that reduce net pro- duction rates. However, unexpectedly the peak pro- ductivity of animal consumers does not coincide with the peak productivity of the producers from which they derive energy. Perhaps this is because many kinds of autotrophic microbes can grow exuberantly 0.1 1 10 Spain S=24101V0.91 100 1000 10000 1 10 Spring size (flow volume: L s1 ) Frequencyofsprings 100 1000 10000 Figure 9 Inverse relationship between frequency of springs in Spain and their size (flow volume, based on class marks of intervals). The power function describing this relationship is shown. The data and equation are from Pe rez ES (1996) Springs in Spain: classification according to their flows and lithologies and their hydraulic contributions. Ground Water 34: 10331041. Figure 10 Macaca fuscata monkeys bathing in Jigokudani Hot Spring in Nagano Prefecture, Japan. Photo by Yosemite (14 February 2005) from Jigokudani_hotspring_in_Nagano_Japan_001.jpg, with permission from Free Software Foundation. 0 0 1 2 Log10annualproduction (kcalm2 ) 3 4 10 20 Spring water temperature (C) 30 40 50 Figure 11 Log10 annual production of producers (autotrophic organisms, ), primary consumers (herbivores, ) and secondary consumers (predators, .) in springs with different mean water temperatures. The consumers include macrofauna only. Polynomial regression lines (all with correlation coefficients >0.96) depict the apparent relationship between productivity and temperature at each trophic level (arrows indicate peak productivity values). The right most value for the secondary consumers is shown in arithmetic form (as a 0) to allow it to be plotted. Data are taken from Cushing CE and Wolf EG (1984) Primary production in Rattlesnake Springs a cold desert spring- stream. Hydrobiologia 114: 229236; Iversen TM (1988) Secondary production and trophic relationships in a spring invertebrate community. Limnology and Oceanography 33: 582592; Krno I, et al. (1998) The influence of organic inputs, acidification and fluctuating discharge on a spring ecosystem. In Bretschko G and Helesic J (eds.) Advances in River Bottom Ecology, pp. 99106. Leiden: Backhuys; Naiman RJ (1976) Primary production, standing stock, and export of organic matter in a Mohave Desert thermal stream. Limnology and Oceanography 21: 6073; Odum HT (1957) Trophic structure and productivity of Silver Springs, Florida. Ecological Monographs 27: 55112; Stockner JG (1971) Ecological energetics and natural history of Hedriodiscus truquii (Diptera) in two thermal spring communities. Journal of the Fisheries Research Board of Canada 28: 7394; Teal JM (1957) Community metabolism in a temperate cold spring. Ecological Monographs 27: 283302; and Tilly LJ (1968) The structure and dynamics of Cone Spring. Ecological Monographs 38: 169197. Hydrology _ Springs 171 at temperatures exceeding 50 C, whereas few hetero- trophic animals can do so (Table 3; Figures 7 and 8). In addition, few animals can subsist on a diet of microbes alone, which would be all that is available at high temperatures. As a result, peak productivities occur at higher temperatures for producers than for consumers. Other specific attributes of springs make them model systems for biologists, as well. Many springs are small, isolated and biotically simple, thus simpli- fying community and ecosystem analyses. As a result, classic studies on energy flow and trophic structure have been carried out in springs, including those used in the analysis described above. Along the length of spring-fed streams, gradients in water temperature, chemical composition, flow rate, or other environ- mental characteristics provide ideal conditions for precisely estimating the environmental tolerances of organisms. In addition, the clear water and physical stability of many springs enables in situ studies of animal behavior and microhabitat selection that are more difficult to do in many other murkier, more unstable aquatic habitats. Island-like properties of springs suit them well for biogeographic and evolutionary studies. Many spe- cies have become highly genetically differentiated in these isolated habitats, and some have evolved major changes in lifestyle, including shifts from terrestrial to aquatic life as in the box turtle Terrapene coahuila of Cuatro Cienagas (Coahuila, Mexico), and from ben- thic scavenging to pelagic filter-feeding as in the amphipod Hyalella montezuma of Montezuma Well (Arizona, USA). The historically spring-fed Lake Xochimilco near Mexico City, Mexico, is home to the axolotl, an entirely aquatic, gill-bearing salaman- der that no longer develops into a terrestrial adult. The axolotl has been a model system in developmen- tal biology for over 100 years. In some places where springs occur in clusters, one can find significant adaptive radiations of microbes, water mites, snails, fishes, and other kinds of organisms. In Yellowstone National Park (Wyoming, USA), new major kinds of life have been discovered, including a new kingdom of life, the Korarchaeota in the domain Archaea, as well as other new major taxonomic groups of viruses and bacteria. Spring archipelagoes also pro- vide excellent systems for metapopulation studies, including the effects of immigration and extinction in local populations on the survival and evolution of species. Some springs that occur in or constitute habitats that are extremely cold, hot, or chemically harsh offer unique opportunities to investigate environmental conditions resembling those of ancient earth or other planets such as Mars. For example, many hot springs contain prokaryotic microbial communities that are free of interactions with plants, animals, and other eukaryotic organisms, just as is thought to have occurred early in the history of life before eukaryotes had evolved. Stromatolites and other mineral-rich microbial deposits found in hot or carbonate-rich springs are reminiscent of those that were common in the Precambrian era. Hot springs may also provide insights into the origin of life because the earliest life forms evolved when the earth was warmer than it is now, and many hot- spring microbes occur near the bottom of lifes evolu- tionary tree. In addition, the harsh environments of hot, acidic, sulfur-rich, and arctic-permafrost saline springs are supplying clues about the conditions under which extraterrestrial life may survive. Valuable environmental science research is also possible at springs. Since spring water is emergent ground water, it provides a window into the quality of underground water sources. Springs provide pure water that is used as a medium in laboratory ecotoxi- cology studies. Thermal and CO2 springs are useful systems for investigating the effects of global warm- ing and greenhouse gases on ecological processes. The chemical and biological composition of sediments deposited at springs can be used as indicators of the history of local environments, including climate, water quality, and land use. And conservation efforts in general have been energized by publicity relating to the plight of endangered spring-dwelling species, such as the pupfish Cyprinodon diabolus, which is only found in Devils Hole (Nevada, USA), the smallest known habitat of any vertebrate species. Threats to this habitat resulting from lowering of the groundwater table have alerted the public to the importance of protecting habitats, not just individual species. Cultural and Societal Importance For ages, springs have benefited humans, and their beauty and the purity of their life-giving waters have engendered mystical, reverent feelings in cultures all over the world. Springs have been regarded as sacred, magical places haunted by spirits, and thus have been the focus of special religious celebrations and cere- monies. In the Yucatan Peninsula of Mexico, the Mayans believed that sinkhole springs (cenotes) are bridges between the physical (surface) world and the invisible (spirit) world, with which they could connect by throwing gifts into them or by making ritual sacrifices. Similar beliefs in other regions of the world have led to the popular notions of wishing 172 Hydrology _ Springs wells and holy water, and in some places shrines have been constructed near or around springs. Many people have believed that spring water has special healing powers and can prolong life, and hence the Spanish explorer Ponce de Leons famous search for the fountain of youth in Florida. Numer- ous medical studies have provided evidence that the mineral properties of some kinds of spring water have therapeutic value especially for skin, arthritic, respiratory, and gastrointestinal ailments. Bathing in warm, mineral spring waters at spas has been and continues to be very popular worldwide. The scien- tific field of balneology has been established to explore the health benefits of these activities. Springs have been significant throughout human history as stopping points along trails and migration routes and for settlements. Need for water has resulted in the establishment of many villages and towns near springs. For example, Figeh spring supplies all of the water for Damascus (Syria), thought to be the oldest continually inhabited city in the world. Countless households, farms, and industries use spring water for drinking, cropland irrigation, livestock watering, brewing, bottling, pro- cessing of materials, and many other purposes. Hot springs are also a source of geothermal energy, which is exploited by many countries, especially in cold regions of the world such as Iceland. In Yugoslavia, flowing springs are used to generate electrical power. The economic importance of springs is enormous both regionally and globally. In 2002, the impact of four of the largest springs in Florida (USA) on local economies amounted to over $65 millions in spend- ing, and over $1 billion in employment. The global economic importance of springs has not been esti- mated, but bottling of spring water alone generates revenue of billions of dollars per year. The organisms found in springs may both benefit and harm humans. Springs have been used as hatch- eries for edible sport fishes, such as trout. Hot springs, in particular, have supplied organisms that have important uses in medicine, industry, biotech- nology, and bioremediation. For example, the doctor fish Garra rufa, which lives in hot springs of Kangel, Turkey, eats dead flaking skin and thus is being used to treat the skin disease psoriasis. In addition, the heat-tolerant bacterium Thermus aquaticus (Taq) isolated from a Yellowstone hot spring is the original source of the Taq polymerase used to amplify DNA in vitro in molecular biology laboratories around the world. This polymerase chain reaction (PCR) now sup- ports a biotechnology industry worth hundreds of mil- lion dollars per year. However, on the downside, some thermal springs may harbor pathogens, such as those causing pneumonia, meningitis, and legionellosis. Many springs are ideal for swimming, fishing, boating, and other forms of recreation. Some attract thousands of tourists every year, such as Silver Springs (Florida) famous for the teeming aquatic life in its crystal clear waters that can be easily viewed through glass-bottom boats. Silver Springs has even been the location for several movies and television shows. Conservation of Springs Springs contribute greatly to the aquatic biodiversity of an area, especially in arid regions. Many endemic and endangered species are found in springs. For example, a large proportion of the estimated $450 species of native freshwater snail species in North America are spring-dwellers, including over 120 spe- cies of springsnails in the hydrobiid genus Pyrgulopsis alone. A recent survey has shown that nearly 80% (158 of 199) of the aquatic animal species endemic to the Great Basin Region of the United States primarily inhabit springs, and many of these species are declin- ing due to human disturbance. Throughout the world, springs are not being prop- erly managed and conserved, and are disappearing rapidly, especially in arid regions (Figure 12). Major threats to springs and their inhabitants include human draining and diversion of groundwater sources, pollu- tion, habitat alteration, and invasive species. Public awareness of the loss of these valuable resources is much needed, to avoid another potential tragedy of silent springs. 1900 1920 1940 Annualflow(millionsm3) Year 10 0 20 30 40 50 60 70 Canals concrete- lined 1912 No flow since March 1961 First cessation of flow Sept. 1955 6200 acres irrigated 19211946 Irrigation began 1900 1960 Figure 12 The demise of Comanche Springs at Fort Stockton, Pecos County, Texas, USA. Although this spring had supplied abundant water to the Comanches and other American Indians for ages, excessive pumping of water from its aquifer caused it to stop flowing permanently in the 1960s. Data from Brune G (2002) Springs of Texas, volume I. College Station: Texas A&M University Press. Hydrology _ Springs 173 Glossary Age of spring water The time it takes water to move from recharge to discharge areas. Aquifer Underground porous rock and cavities where water is stored. Aquifers receive water from precipitation and surface waters, and supply water to springs. Archaea and bacteria These mostly single-celled organisms are the two major types of prokaryote organisms (characterized by simple cells lacking nuclei and other organelles). They constitute two of the three major branches (domains) of life; the third branch is the eukarya, which includes the protists, fungi, plants and animals, all of which are made of more complex eukaryotic cells that have nuclei and other organelles. The archaea and bacteria are found almost everywhere on earth, though the archaea are especially common in extreme environments, including very hot and chemically caustic habitats. Balneology Study or practice of using mineral (spring) water to treat and cure diseases and other ailments. Typically involves bathing. Base flow Water flowing through a spring that comes from the storage reservoir of an aquifer dur- ing periods of low precipitation (recharge). Base flow tends to be more constant than overflow that results from flooding events during periods of high precipitation (recharge). Biota Living organisms of all kinds in a specific area. Contact zones Flat surfaces separating different rock layers (strata). Also called bedding planes. Cyanobacteria Photosynthetic bacteria sometimes called blue-green algae. Discharge The volume of water flowing into and through a spring (or other flowing waters). Dolomite A soluble, sedimentary rock chiefly com- posed of the mineral Ca,Mg(CO3)2. Often found in karstic landscapes. Fauna Animal life in an area. Fissures and fractures Cracks, breaks or disconti- nuities in rocks. Include faults along which rock has moved, and joints along which no movement of rock has occurred. Flora Plant life in an area. Hydrologic cycle The circulation of the Earths water molecules between the atmosphere, soil, living organisms, bodies of surface water, and reser- voirs of ground water (also called the water cycle). Precipitation moves water from the atmosphere to the Earths surface (including soil and sur- face waters); infiltration and gravity-driven re- charge moves water from the Earths surface to ground waters; absorption and other uptake pro- cesses move water from the atmosphere, soil and surface and ground waters to living organisms, dis- charge moves water from ground waters to soil and surface waters, evaporation moves water from soil, surface waters and other objects on the land surface to the atmosphere; and evaporation, tran- spiration and excretion move water from living organisms to the atmosphere, soil, and surface and ground waters. Hydrology The study of water resources and the hydrologic cycle, including the properties, move- ment, distribution and effects of water on geologi- cal features throughout the Earth. Interstitial Spaces between sediment particles. Karst terrains Characterized by the strong effects of the aqueous dissolving of bedrock minerals, result- ing in landscape depressions and complex surface and underground drainage patterns (including caves, sinkholes, springs, and sinking streams). Usu- ally composed largely of carbonate rocks, chiefly calcareous such as limestone and dolomite, but may also arise in gypsum, salt, silica and other rocks. Lentic Associated with lakes and ponds. Limestone A soluble, sedimentary rock chiefly com- posed of the mineral calcite (CaCO3). Often found in karstic landscapes. Lotic Associated with flowing waters, such as streams and rivers. Macroinvertebrates Animals without back- bones that usually grow longer than 0.5 mm in body length and can readily be seen with the naked eye. Macrophytes Aquatic plants that are partially or completed submerged in water. Metapopulation Regional cluster of patchy popula- tions of the same species that engage in interchange of individuals by migration. Microinvertebrates Animals without backbones that usually do not grow longer than 0.5 mm in body length and are generally best seen with a microscope. 174 Hydrology _ Springs Recharge The gain of water by an aquifer from precipitation and surface waters. Runoff Water appearing in streams directly from precipitation on land surfaces. Runoff streams tend to have more variable flow rates than springs fed by groundwater reservoirs. Sinkhole A natural depression in the landscape often containing exposed ground water at its bot- tom. Caused by the subsidence or collapse of sur- face soil, sediment or rock as a result of the dissolving of underlying rock strata (e.g., limestone and dolomite) by ground water. Stromatolites Multi-layered sedimentary structures that grow as domes, columns, cones or branching structures as a result of the activity of microorgan- isms (especially cyanobacteria) and (or) various abiotic processes. Stromatolites were common in the Precambrian era and their fossils represent some of the earliest life forms in the geological record. Stromatolites are presently rare, growing in harsh environments where animal grazing is ex- cluded (e.g., hot springs and highly saline lakes and marine lagoons). Trophic structure Feeding relationships among species in an ecological community. Includes the net- work of flow of energy and materials from autotro- phic organisms, which make their own food from inorganic materials ( producer trophic level), to heterotrophic herbivores, predators, parasites and detritivores, which use other organisms or organic materials as food ( consumer trophic levels). Vertebrates Animals with backbones, such as fish, amphibians, reptiles, birds and mammals. See also: Acidification; Alkalinity; Aquatic Ecosystems and Human Health; Atmospheric Water and Precipita- tion; Bioassessment of Aquatic Ecosystems; Biological- Physical Interactions; Carbon, Unifying Currency; Chemi- cal Fluxes and Dynamics in River and Stream Ecosystems; Chloride; Currents in Rivers; Dissolved CO2; Distribution and Abundance of Aquatic Plants Human Impacts; Flow Modification by Submerged Vegetation; Fluvial Export; Fluvial Transport of Suspended Solids; Gas Exchange at the Air-Water Interface; Ground Water; Ground Water and Surface Water Interaction; Groundwater Chemistry; Hydro- logical Cycle and Water Budgets; Light, Photolytic Reactiv- ity and Chemical Products; Major Cations (Ca, Mg, Na, K, Al); Mercury Pollution in Remote Fresh Waters; Methane; Natural Organic Matter; Pollution of Aquatic Ecosystems I; Pollution ofAquatic Ecosystems II: Hydrocarbons, Synthet- ic Organics, Radionuclides, Heavy Metals, Acids, and Thermal Pollution; Rivers; Salinity; Silica; Streams. Further Reading Botosaneanu L (ed.) (1998) Studies in Crenobiology: The Biology of Springs and Springbrooks. Leiden: Backhuys. Cantonati M, Gerecke R, and Bertuzzi E (2006) Springs of the Alps sensitive ecosystems to environmental change: From biodiversity assessments to long-term studies. Hydrobiologia 562: 5996. Chapelle FH (1997) The Hidden Sea: Groundwater, Springs, and Wells. Tucson, AZ: Geoscience Press. Ferrington LC (ed.) (1995) Biodiversity of aquatic insects and other invertebrates in springs, Journal of the Kansas Entomological Society 68 (Supplement): 1165. Glazier DS (1991) The fauna of North American temperate cold springs: Patterns and hypotheses. Freshwater Biology 26: 527542. Hinterlang D (ed.) (1996) 1st European Symposium of Spring Ecology and Conservation, Crunoecia 5: 1304. Hynes HBN (1970) The Ecology of Running Waters. Toronto: University of Toronto Press. LaMoreaux PE and Tanner JT (eds.) (2001) Springs and Bottled Waters of the World: Ancient History, Source, Occurrence, Quality and Use. Berlin: Springer-Verlag. Marsh PC (ed.) (1984) Proceedings of a special symposium: Biota of Cuatro Cienegas Coahuila, Mexico, Journal of Arizona- Nevada Academy of Science 19: 189. Meyer JL, Strayer DL, Wallace JB, Eggert SL, Helfman GS, and Leonard NE (2007) The contribution of headwater streams to biodiversity in river networks. Journal of the American Water Resources Association 43: 86103. Renaut RW, Jones B, et al. (2003) Special issue: Sedimentology of hot springs. Canadian Journal of Earth Sciences 40: 14391738. Reysenbach AL, Voytek M, and Mancinelli R (eds.) (2001) Thermophiles: Biodiversity, Ecology and Evolution. New York: Kluwer. Sada DW, Williams JE, Silvey JC, Halford A, Ramakka J, Summers P, and Lewis L (2001) Riparian area management: A guide to managing, restoring, and conserving springs in the western United States, Technical Reference, pp. 173717. Denver, CO: United States Department of the Interior Bureau of Land Management. Smart C and Worthington RH (2004) Springs. In: Gunn J (ed.) Encyclopedia of Caves and Karst Science, pp. 699703. New York: Taylor and Francis. Waring GA, Blankenship RR, and Bentall R (1965) Thermal springs of the United States and other countries of the world A summary. Geological Survey Professional Paper 492. Washington, DC: United States Government Printing Office. Williams DD and Danks HV (eds.) (1991) Arthropods of springs, with particular reference to Canada, Memoirs of the Entomo- logical Society of Canada 155: 1217. Zeidler W and Ponder WF (eds.) (1989) Natural History of Dal- housie Springs. Adelaide: South Australian Museum. Relevant Websites Springs and the water cycle. Freshwater springs and their uses in research and teaching. Australias desert springs, with special emphasis on fishes. Hydrology _ Springs 175 Biota of Illinois caves and springs. spring.htm Springs of the Suwannee River Water Management District in Florida, with much basic information. Information about hot springs. Life at high temperatures, especially in the hot springs of Yellowstone National Park. page03.html Microbial observatory at sulfide- and methane- rich Zodletone Spring, Oklahoma. Floridas springs: protecting nat- ures gems. Managing spring wetlands for fish and wildlife habitat. Rare aquatic snails in springs of the southwestern United States. 176 Hydrology _ Springs Wetland Hydrology R W Tiner, University of Massachusetts, Amherst, MA, USA 2009 Elsevier Inc. All rights reserved. Introduction Wetland hydrology frequently occurring prolonged inundation and/or soil saturation (waterlogging) is the driving function that creates and maintains wetlands and provides wetlands with unique qualities and significant ecological functions that are highly valued by society. Wetlands may be generally defined as shallow water areas or lands that are periodically flooded or saturated long enough to support hydro- phytic vegetation and/or other forms of aquatic life. Conceptually, wetlands lie between dry land and deep water and as a result have often been referred to as ecotones (a transitional habitat; part land, part water). Depending on the wetland type, the wetland may be subjected to flooding or soil saturation or a combination of both. From a hydrologic standpoint, wetlands encompass a wide range of wetness con- ditions from permanent to periodic inundation or waterlogging. Differences in climate, geologic setting, and other factors have created a diversity of wetland types globally with varied hydrologies that affect plant and soil development, their use by wildlife, their functions and values. This article is a general introduction to wetland hydrology for a nontechnical audience; for more advanced coverage, consult Further Reading. Since the focus of this encyclopedia is on inland waters, the discussion of wetland hydrol- ogy emphasizes that of inland wetlands (nontidal wetlands and tidal freshwater wetlands) and does not address marine and estuarine wetlands. Water Sources Nontidal wetlands receive water from meteoric sources (precipitation, snow, sleet, hail, fog, and mist) or tellu- ric sources (ground water), while tidal wetlands receive a significant inflow of water from tides in addition to the other sources. Meteoric sources affect all lands, but for wetlands to form, water must persist either on the surface or in the soil for sufficient time to promote the colonization, growth and survival of hydrophytic vegetation and the development of hydric soils and substrates, and to create environmental conditions that support other aquatic life. Factors Contributing to Wetland Hydrology Topography (landform), landscape position (proxim- ity to a water source), soil properties, geology, and climatic conditions are important factors in wetland formation. Depressions and broad flats with poor drainage are places where water can accumulate in sufficient quantities to create wetlands. Mountainous areas tend to have less wetland than coastal and glaciolacustrine plains largely due to drainage proper- ties (e.g., rainwater drains readily from slopes and collects on flats). Wetlands in mountainous areas likely receive considerable groundwater inflow (groundwater wetlands), while wetlands on broad flats in areas of high rainfall may be supported by rainwater (surface water wetlands; Figure 1) or ground water. Inland wetlands occur (1) along the shores of lakes and ponds where high water levels and the presence of a permanent waterbody lead to permanent inundation of shallow water zones and periodic inundation of low- lying neighboring areas, (2) on floodplains where they are subject to seasonal inundation, (3) in depressions that receive runoff from adjacent areas and ground- water discharge, (4) on broad flats of coastal plains or glaciolacustrine plains where drainage is poor, (5) at toes of slopes where subsurface water reaches the sur- face, (6) on slopes associated with springs and seeps where ground water discharges to the surface, (7) in paludified landscapes where low evapotranspiration and an excess of water allow peat mosses to grow over once dry land covering the landscape with peat (e.g., blanket bogs), (8) in permafrost areas where fro- zen soils serve as an impermeable layer that perches water at or near the surface, and (9) in areas below glaciers and snowfields where the seasonal flow of meltwater creates wet conditions. Soils with low hydraulic conductivity such as clayey soils and soils with restrictive layers (e.g., hardpans) near the surface favor wetland development over sandy soils that tend to have good internal drainage due to large effective porosity (high hydraulic conductivity). Sandy soils become wet if external drainage is poor or if periodi- cally flooded for long duration or saturated by water from external sources (e.g., regional water tables). Geological features, such as contacts between different 177 rock types that outcrop along hillsides, create condi- tions favoring the formation of seeps and associated wetlands where ground water or near-surface interflow intersects the land surface. Desert spring-fed wetlands are the result of groundwater discharge from region- al aquifers. Dissolution of limestone formations allow for the establishment of wetlands in karst terrain. Morainal deposits in glaciated regions typically create deranged (nonintegrated) drainage patterns that produce isolated depressions on low-permeability substrates where wetlands develop, whereas kettle basins in outwash deposits will also produce wetlands where such basins are in contact with aquifers. Precipi- tation patterns significantly influence wetland forma- tion. Wetlands are naturally more abundant in regions with warm humid climates than in hot arid climates for obvious regions. The latter regions may support ephemeral wetlands during extremely wet years that create conditions in landscape positions that typically support wetlands in humid regions. Groundwater depressional wetland Surface water depressional wetland Groundwater slope wetland Surface water slope wetland Overland flow Groundwater inflow Seasonal high water table Evapotranspiration Precipitation Overland flow Water table (may temporarily rise to wetland level, but groundwater inflow is minor compared to surface water inflow) Evapotranspiration Precipitation Overland flow Water table Groundwater inflow Streamflow Evapotranspiration Precipitation Overland flow Water table (may temporarily rise to wetland level, but groundwater inflow is minor compared to surface water inflow) Lake or river flood water level Evapotranspiration Precipitation Figure 1 Four types of wetlands defined by wetland hydrology and topography: groundwater depressional wetland, groundwater slope wetland, surface water depressional wetland, and surface water slope wetland. Following this approach, wetlands on broad flats may be considered surface water flat wetlands; they are not inundated (except in microdepressions) but have seasonal high water tables. Source: Tiner RW (1988) Field guide to nontidal wetland identification. Newton Corner, Massachusetts, USA: U.S. Fish and Wildlife Service and Maryland Dept. of Natural Resources. Reprinted by Institute for Wetlands and Environmental Research, Inc., Leverett, MA; redrawn from Novitski RP (1982) Hydrology of Wisconsin wetlands, Information Circular 40. Reston, VA: U.S. Geological Survey. 178 Hydrology _ Wetland Hydrology How Wet is a Wetland? One would think it would be relatively easy to define a wetland from a hydrologic standpoint; after all if an area is wetland, it must be wetter than dry land. Yet to fully describe and understand hydrology requires long-term measurements and for wetlands this in- volves monitoring water tables (soil saturation) as well as surface water. Given the diversity of wetland types, that wetlands are transitional habitats between dry land and open water, and the need to conduct studies over long time periods, it is little wonder that such information is lacking for most wetlands and that it is not a simple matter to define the minimum wetness of wetland. Both surface and groundwater sources need to be considered in determining minimum wetness for defining wetland hydrology. Scientists in the United States probably have spent more time contemplating this topic because wetlands on both public and pri- vate lands are regulated by the federal government and by many state and local governments. Such regu- lation requires identifying specific limits of wetlands on the ground. To be a wetland for jurisdictional purposes, an area typically must have a positive indi- cator of hydrophytic vegetation, hydric soils, and wetland hydrology. The former two features are mani- festations of wetland hydrology and serve as valid indicators of wetlands in the absence of drainage. Yet, many situations are encountered where some drainage has been performed, thereby raising the ques- tion is the area still wet enough to be identified as wetland? In such areas, the plants and soils may better reflect past hydrologic conditions and may no longer be valid indicators of current site wetness. So to answer this question, wetlands hydrology must be defined and a lower threshold of wetness established. (Note: The upper threshold of wetness clearly is permanent inun- dation or saturation to the surface.) Wetland Hydrology Defined A group of distinguished American wetland scientists studied the topic of wetland delineation for 2 years and came up with the following definition: An area has wetland hydrology when it is saturated within one foot of the soil surface for two weeks or more during the growing season in most years (about every other year on average). Depth of Saturation Roots supply plants with nutrients and water needed for growth and reproduction. Heavy rains that saturate the soil for as little as a few hours can cause root hairs to die of oxygen starvation as evidenced by wilting of vegetable crops (e.g., squash and cabbages) after rainfall. Prolonged saturation and accompanying anaerobic conditions adversely affect root function, causing changes in root morphology (aerenchyma de- velopment), root rot and dieback, and the formation of shallow roots (near the surface). Since they live in areas of frequent soil saturation, wetland plants have most of their roots located in the upper, partly aerated zone of the soil. This zone is typically within 30 cm (1 ft) of the soil surface. Duration of Wetness Although flooding for as little as a day can create anaerobic conditions under special circumstances in some soils, most plants need to be wet longer to adversely affect their growth and survival. Some wet- land plants begin to develop morphological properties (e.g., aerenchyma tissue, adventitious roots, and hypertrophied lenticels) within 12 weeks of flooding or waterlogging. Soil scientists have identified long and very long durations as important periods of flood- ing for soils. Long duration is defined as inundation from 7 to 30 days, while very long duration is longer than 30 days. Flooding (from overbank flows or run- off) or ponding (standing surface water in a closed depression) for long duration or more during the growing season in most years can be used to identify a hydric (wetland) soil regardless of its morphological properties. Frequency of Prolonged Wetness In order to be a wetland under most definitions, an area has to be frequently wet, which has been defined as every other year on average. This definition works for wetlands in humid regions where average condi- tions may have some significance. Yet for arid and semiarid regions, this definition is problematic, for such regions may experience long-term droughts that have a profound effect on the average. In these regions, a series of wet years can create conditions long enough for wetlands to become established. While there are typical wetlands supported by springs and river overflows in these areas, some wetlands are ephemeral types showing up only during periods of extreme wetness. The term episodic has been applied to describe such wetness and these infre- quently wet areas are viewed as wetlands in some countries (e.g., Australia). Soils in arid regions may develop hydromorphic properties when saturated for less than 5 weeks at a frequency of once every 3 years. Hydrology _ Wetland Hydrology 179 Growing Season Although the wetland hydrology definition is explicit in stating the frequency and duration of wetness and the depth of saturation, the seasonality of wetness growing season can be defined in many ways which could lead to different interpretations of wetland hydrology. For example, the growing season has been traditionally used in agriculture to assist in deter- mining planting times for crops like corn, wheat, and rice. As such, the growing season could be defined as the frost-free period where there would be virtually no risk of crop failure due to frost or freeze. This concept is not useful for natural plant communities that are adapted to local environmental conditions. For exam- ple, by the time the frost-free period arrives, many native plants have already flowered and leafed-out. So, from an ecological standpoint, the growing season has commenced well before there is no risk of frost. The growing season is actually a concept that is best applied to a particular plant. What is the growing season for red maple (Acer rubrum) or corn (Zea mays)? Such a definition would be based on when they initiate new growth after a period of dormancy. Yet, this concept is also not useful for defining wetland hydrology. Given that the focus of wetland hydrology is often to define conditions that affect plant establish- ment, growth, and survival, and sometimes the forma- tion of hydric soils, the time of year should, at least, be related to plant activity and possibly to soil formation processes. From the botanical standpoint, one could say the start of the growing season for wetlands should be predicated on the vegetation growing in wetlands. Observations of plant growth in wetlands would therefore serve as valid indicators that the growing season has begun. The earliest of the plants that leaf out or flower in spring (e.g., willows Salix spp., alders Alnus spp., marsh marigold Caltha palustris, leatherleaf Chamaedaphne calyculata, and skunk cabbage Symplocarpus foetidus) would be the best indicators for determining this. A more generalized approach would be to consider the growing season for an area to have commenced when any plants (wet- land or upland) show signs of growth (e.g., budbreak, leaf emergence, or blooming). The end of the growing season should be defined by the end of plant growth in wetlands or in the local area. Recognizing that the fall is an important time for root growth, the growing season extends beyond the time when leaves fall off deciduous-leaved plants. In all likelihood, it continues until the ground freezes. Minimum temperatures for root growth may be from slightly above 07 C (3244.6 F), with optimum temperatures ranging from 10 to 25 C (5077 F). Soil scientists have used the term biologic zero to define conditions that relate to microbial activity in the soil: 5 C (41 F) degrees measured at a depth of 50 cm (20 in.) in the soil. This concept may have some utility in temperate and tropical regions, but it is not valid for subarctic and arctic regions where permafrost or fro- zen soil occurs at shallow depths and therefore no growing season would exist. Despite the significance of flooding and soil satura- tion on growth of nonevergreen plants, there are other factors to consider when defining wetland hydrology (i.e., should the focus be on growing sea- son or year-round conditions?). For example, what are the needs of wetland-dependent animals and are significant wetland functions being performed out- side the growing season. Consider the following: 1. Evergreen plants and persistent graminoids (grass and grasslike plants) continue to grow during the dormant period for nonevergreens and satura- tion during this time should have some effect on these and competing species. 2. Water conditions during the dormant period have a profound influence on hydrologic conditions during the early part of the growing season and may prevent winter dessication of some plants. 3. Hydric soil properties have developed under reducing conditions that extend beyond the growing season. 4. Critical activities of some animals require dormant season flooding or soil saturation (e.g., woodland vernal pool breeders and pond animals). 5. Aquatic animals like fish need water year round and are active year round. 6. Wetland functions such as nutrient transformation and cycling, shoreline stabilization, surface water detention, and sediment retention are independent of the growing season. 7. Wetness limitations during the dormant period also affect the potential uses of the land. Defining wetland hydrology based on year-round conditions appears to be justified from ecological and functional perspectives. This approach also would better reflect how wet some of the drier-end wetlands really are. Many of these drier-end wetlands (e.g., wet flatwoods of the southeastern United States) are wet for significant periods (months) during the year, but are saturated near the surface for relatively short periods (weeks) during the growing season. Does Prolonged Saturation Guarantee Anaerobic and Reducing Conditions? Although the definition of hydric soil emphasizes anaerobic reducing conditions and most wetlands 180 Hydrology _ Wetland Hydrology are exposed to periodic anaerobiosis, there may be some situations where wetlands exist in aerobic envir- onments. Also, soils saturated for long periods are not always reduced; there must be a source of organic matter, sufficiently high temperatures to support microbial activity responsible for reduction, and a population of reducing microbes present. (Note: The latter is typically present if the first two conditions are satisfied.) Possible aerobic wetlands occur in seep- age areas where oxygenated water is continuously flowing downhill, especially in colder climates and high-elevation sites, and along coldwater mountain streams on cobble-gravel or sandy substrates. Saturated soils may not be reduced under the follow- ing circumstances: (1) in cold climates with average temperatures of less than 1 C (33.8 F), (2) in very saline waterlogged desert soils where salinity restricts growth of reducing microbes, (3) in areas with little or no organic matter and moderate to high levels of calcium carbonate (e.g., irrigated rice basins in north- west India lack a low chroma matrix soil), and (4) in areas subject to groundwater discharge where dis- solved oxygen is present in water (e.g., in areas of moderate relief and soils on the edges of valleys). Wetland Water Regimes The hydrology of wetlands can be described in numerous ways. The duration of flooding and soil saturation can be defined by various water regimes (Table 1). The flow of water can be classified as inflow (water coming into a wetland with no outlet; a sink), outflow (water flows out of wetland; source), throughflow (water comes into and exits wetland), and bidirectional flow (water levels rise and fall in wetlands due to tides, lake or pond levels). If the wetland is surrounded by dry land and there is no known flow into or out of the wetland (besides runoff and near-surface flow from adjacent upland), the wetland is hydrologically isolated from a surface- water perspective, but it may not be hydrologically isolated from a groundwater perspective. The topo- graphic position of isolated wetlands may determine whether they are sources, throughflows, or sinks based on their location in groundwater flow systems. In semiarid regions like the North American Prairie Pothole Region, topographic position and local geol- ogy influence water salinity and vegetation patterns, with freshwater wetlands at the highest elevations or levels of the groundwater flow system (sources), the most saline wetlands at the lowest levels (sinks or sumps), and flow-through wetlands with intermedi- ate salinities in between (Figure 2). Because salt toler- ance is an adaptation possessed by certain plants, vegetation can be used to infer the hydrologic func- tion in these regions. Hydrographs for Different Wetland Types Due to variations in climate, soils, vegetation, geologic setting, and other factors, the presence of water and its location in wetlands varies around the globe. Even within local areas, the hydrology of wetlands differs Table 1 Inland wetland hydrology descriptors based on the U.S. Fish and Wildlife Services wetland classification system Water regime modifiers General definition Permanently flooded* Inundated continuously, year-round in all years Intermittently exposed Inundated year-round in most years, but exposed during extreme droughts Semipermanently flooded* Inundated throughout the growing season in most years Seasonally flooded* Inundated for extended periods during the growing season, but usually not flooded later in the growing season; water table may be near the surface for much of the time when not flooded (seasonally flooded/ saturated) or may be well below the surface Temporarily flooded* Inundated for brief periods during the growing season (usually a couple of weeks or less early in the growing season), with the water table typically well below the surface for extended periods thereafter Intermittently flooded Inundated for variable periods with no detectable seasonality; area is usually exposed Saturated Water table is at or near the surface for most of the growing season and surface water usually absent; when soil is saturated only seasonally, usually early in the growing season, the hydrology is referred to as seasonally saturated Artificially flooded The frequency and duration of inundation is controlled by humans; in the strictest sense, the control is purposeful by means of pumps or siphons, but more generally, wetlands flooded by any artificial means qualify, including irrigation An asterisk (*) denotes water regimes that can also be modified to describe freshwater tidal wetland hydrology by adding -tidal to the term (i.e., permanently flooded-tidal, semipermanently flooded-tidal, seasonally flooded-tidal, and temporarily flooded-tidal). Adapted from Cowardin LM, Carter V, Golet FC, and LaRoe ET (1979) Classification of Wetlands and Deepwater Habitats of the United States. Washington, DC: U.S. Fish and Wildlife Service, FWS/OBS-79/31. Hydrology _ Wetland Hydrology 181 by wetland type. Some wetlands are permanently flooded or nearly so, others are never flooded but permanently saturated, and the rest are either periodi- cally inundated or seasonally saturated. The fluctua- tions of the water table and water levels in wetlands may be depicted graphically by hydrographs (Figure 3). Changing Water Levels Site wetness varies seasonally, annually, and long- term. Seasonal changes are reflected in the hydro- graphs that clearly show the wet season and dry season for certain wetland types. Some types are per- manently flooded or saturated near the surface with the latter showing slight changes in water table dur- ing the dry season (e.g., summer in the northeastern United States). Other types show marked fluctuations in the water table during the year. Wetlands also experience changes from year to year. During wet years, water tables are higher than normal and water may persist on the surface for longer periods, while in dry years they are lower (Figure 4). The long-term hydrologic cycle encompasses years of normal precipitation, above normal precipita- tion and below normal precipitation. If wetland hydrology were monitored for decades, the effect of these precipitation patterns on wetland water levels and water tables could be readily seen. Unfortunate- ly such data are lacking for most wetland types. Water levels in wetlands along the shores of North Americas Great Lakes fluctuate with changes in lake levels which vary from about 12 m (3.56.5 ft) from extremely wet years to extremely dry years. These changes have a significant impact on plant commu- nities with aquatic beds predominating in high water years and wet meadows in low water years (Figure 5). Many woody plants that colonize these wetlands dur- ing dry years are killed by high water during wet years. These wetlands are among the most dynamic of inland wetlands in North America from a plant composition standpoint. Wetlands in arid and semi- arid regions (e.g., prairie potholes and playas) also experience somewhat similar vegetation changes due to variability in regional precipitation patterns. Water Budget The water budget of an area, wetland or nonwetland, is an accounting of water inflows (gains or inputs) and outflows (losses or outputs) to determine the change in storage (Figure 6). Inputs include water sources (precipitation, surface water, and ground water), Recharge wetland Recharge wetlandFlow-through wetland Discharge wetland Explanation Regional flow Local flow Local flow Intermediate flow Intermediate flow Direction of groundwater flow Average water table Flow-through wetland Discharge wetland Figure 2 Groundwater flow patterns in North American prairie pothole wetlands. Characteristics of the three types shown differ: recharge wetlands (that recharge ground water) are more fresh and have standing water for only a few months, whereas discharge wetlands (that receive ground water) are the most saline and are permanently flooded and flow-through wetlands are intermediate in salinity and duration of surface water. Source: Berkas WR (1996) North Dakota wetland resources. In: Fretwell JD, Williams JS, and Redman PJ (eds.) National Water Summary on Wetland Resources, Water-Supply paper 2425, pp. 303307. Reston, VA: U.S. Geological Survey. 182 Hydrology _ Wetland Hydrology while outputs or water losses are attributed to evapo- ration, transpiration by plants, surface and subsurface water runoff, and groundwater recharge. Because wet- lands have an excess of water, at least seasonally, the inputs are greater than the outputs at such time. The water budget equation is used by hydrologists and other scientists to evaluate the net change of the volume of water in a defined area over time. Change in volume is the sum of the inputs minus the sum of the outputs as expressed by the following equation: V P Si Gi Ti ET So Go To Inputs The four sources of water are precipitation (P), sur- face water inflow (Si), groundwater inflow (Gi), and 6 4 2 0 Jan Feb Mar Apr May June July Aug Sep Floodplain forest Ground level Ground level Ground level Ground level Ground level Ground level Fen or bog Wet meadow Marsh Flatwood Hardwood swamp Oct Nov Dec 4 2 0 4 2 0 Positionofwatertable (feedaboveorbelowgroundlevel) +2 +2 1 0 +1 1 2 3 0 +1 0 +1 +2 +3 +4 Figure 3 Hydrographs of some common wetland types in the northeastern United States. Note that there is considerable variability within types that are not reflected in these hydrographs and that these hydrographs are intended to represent general tendencies in water levels for illustration purposes. Source: Tiner RW (2005) In Search of Swampland: A Wetland Sourcebook and Field Guide. New Brunswick, NJ: Rutgers University Press. Hydrology _ Wetland Hydrology 183 Soil surface Depth below surface (inches) 0 20 40 60 80 A M Surface water present for variable periods Active plant growth and increasing evaporation Plants dormant lower evaporation Water table Surface water present for variable periods J J A Year 1 Year 2 S O N D J F M A M J J A S O N D Figure 4 Seasonal and annual differences in water levels in a forested wetland in the northeastern United States. Note that Year 1 is a year of normal precipitation, while Year 2 represents a wet year, with corresponding changes in water table levels. Sources: Tiner RW, and Burke DG (1995) Wetlands of Maryland. National wetlands inventory cooperative publication. Hadley, MA: U.S. Fish and Wildlife Service, Northeast Region and Maryland Dept. of Natural Resources; based on data from Lyford WH (1964) Water table fluctuations in periodically wet soils of central New England, Harvard forest paper No. 8. Petersham, MA: Harvard University Forest. Feet Southwest Drowned sedges 1973 (High water) Water level Fine grained deposits 1977 (Falling stage) 1965 (low water) Extensive meadow Peat accumulation ? Old channel Emergent marsh Betsie river Clay Sand Marl 177.5 177.0 176.5 176.0 175.5 177.5 177.0 176.5 176.0 175.5 Water level Sand Sand Peat Die back Northeast Meters 177.5 177.0 176.5 176.0 582 580 578 582 580 578 576 582 Shrub zone Water level 580 578 576 0 250 500 750 1000 0 100 200 300 1250 400 1500 500 1750 2000 600 2250 ft 700 M ? Figure 5 Vegetation dynamics in a Great Lakes coastal wetland in response to changing lake levels. Source: Herdendorf CE, Hartley SM, and Barnes MD (eds.) (1981) Fish and wildlife resources of the Great Lakes coastal wetlands within the United States, vol. 1: overview. Washington, DC: U.S. Fish and Wildlife Service, Biological Services Program, FWS/OBS-81/02-v1. 184 Hydrology _ Wetland Hydrology incoming or flood tides (Ti). The contributions of these sources vary daily, seasonally, and yearly. Inflows are typically natural, but can be human induced by releases of water from dams and similar inputs. Outputs Water is lost through evapotranspiration (ET), sur- face water outflow or runoff (So), groundwater out- flow or recharge (Go), and outgoing or ebb tides (To). Evapotranspiration is a combination of evaporation and plant transpiration. Evaporation increases with rising air temperature and exposure of the land or water surface to the sun, while plant transpiration is the natural uptake of water from the soil by plants and eventual loss to the atmosphere in the form of water vapor. Groundwater outflow could recharge ground water supplies or result from water with- drawals by humans. Annual Water Budgets Water budgets may be calculated for a wetland or a watershed and for different time periods. As men- tioned, wetlands form in areas inundated or water- logged for long periods of time; the wet season could be from winter to early spring (as it is in the eastern United States), summer to fall (as in Florida and the southwest United States), or in winter (in Mediterra- nean climates like that of California). During the wet season, the inputs would exceed the outputs, so that water is stored in the wetland. When evaluated over a longer period, however, outputs may exceed inputs, especially for wetlands that are nearly permanently wet. Some examples of annual water budgets are shown in Table 2. Wetland Hydrology Indicators In the absence of site-specific hydrological data (e.g., hydrographs or recorded data from water-level gages or observation wells), various features can be used to verify recent flooding or waterlogging. These features may be direct observations of water on the surface or near the soil surface, indirect evidence such as features left by recent flood or saturation events (Table 3), or inferred from soil properties (e.g., hydric soil indicators, presence of a hard pan, dense clay layer, or permafrost layer near the surface) or vegeta- tion (e.g., presence of obligate hydrophytes or plants with certain morphological adaptations to excessive wetness like hypertrophied lenticels and water roots). GWI GWO SWO SWI P ET High water table Low water table S Figure 6 Components of the wetland water budget: P, precipitation; SWI, surface water inflow; GWI, groundwater inflow; ET, evapotranspiration; SWO, surface water outflow; GWO, groundwater outflow; and DS, change in storage. Sources: Carter V (1996) Wetland hydrology, water quality, and associated functions. In Fretwell JD, Williams JS, and Redman PJ (eds.) National Water Summary on Wetland Resources, Water-Supply Paper 2425, pp. 3548. Reston, VA: U.S. Geological Survey. Hydrology _ Wetland Hydrology 185 Table 3 Potential wetland hydrology indicators for North American wetlands Direct Evidence Visual observation of surface water Visual observation of a water table within 30 cm (12 in.) of the surface of nonsandy soils Visual observation of a water table within 15 cm (6 in.) of the surface of sandy soils Visual observation of soil glistening, or shaking or squeezing pore water out of the soil within 30 cm in nonsandy soil or within 15 cm in a sandy soil Positive reaction to a ferrous iron test with 30 cm of the surface in a nonsandy soil or within 15 cm of a sandy soil Observed soil color change when exposed to air due to oxidation of ferrous iron Sulfidic odor (rotten egg smell) from soil sample within 30 cm of the surface Indirect Evidence of Flooding or Ponding Water marks (e.g., blackish stains or silt lines) Drift or wrack lines (piles of water-carried debris) Sediment deposits Algal crusts on or near the ground Drainage patterns (e.g., braided streams, network of minor streams, scoured areas, scouring around roots, and living plants bent over or lying in the direction of water flow) Water-stained leaves Mud cracks or surface polygons Live or dead remains of aquatic invertebrates Presence of crayfish burrows Presence of periphyton (aufwuchs) growing on plants Aerial photo showing flooding or ponding Indirect Evidence of Recent Soil Saturation Oxidized rhizospheres within 30 cm of soil surface (e.g., iron oxide plaques on living roots or redox concentrations in soil surrounding roots) Presence of muck or mucky mineral soil on surface Presence of deep soil cracks in clayey soils (e.g., Vertic soils) Presence of salt deposits on soil surface Presence of redox features in soil horizon despite bioturbation (i.e., mixing of soil by animals like earthworms) Presence of deep impressions in soil left by heavy objects (e.g., vehicles or livestock) Observed water table between 30 and 60 cm (1224 in.) deep during dry season or dry year Note that all these indicators are not of equal stature in verifying that the site still has wetland hydrology. Source Noble CV, Martel DJ, and Wakely JS (2005) A national survey of potential wetland hydrology regional indicators. Vicksburg, MS: U.S. Army Corps of Engineers, Waterways Experiment Station, ERDC TN-WRAP-051. Table 2 Examples of annual water budgets for selected wetland in North America Wetland (location) Inputs Outputs Net storage P Si Gi ET So Go Bog (Massachusetts) 100 70 8 8 14 Cypress River Swamp (Illinois) 23 70 7 22 71 6 1 Okefenokee Swamp (Georgia) 76 23 55 43 2 1 Prairie Pothole Marshes (North Dakota) 48 52 78 22 0 Hidden Valley Marsh (Ontario) 11 53 36 12 35 50 3 Arctic Fen (Northwest Territories) 22 52 26 27 40 32 Experimental Marsh (Ohio) 3 97 2 72 26 0 A positive storage value indicates a net gain in water. Sources Carter V (1996) Wetland hydrology, water quality, and associated functions. In Fretwell JD, Williams JS, and Redman PJ (eds.) National Water Summary on Wetland Resources, Water-Supply Paper 2425, pp. 3548. Reston, VA: U.S. Geological Survey. Winter TC (1989) Hydrologic studies of wetlands in the northern prairie. In Van der Valk A (ed.) Northern Prairie Wetlands, pp. 1654. Ames, IA: Iowa State University Press. Zhang L and Mitsch WJ (2002) Water budgets of the two Olentangy River experimental wetlands in 2001. In Mitsch WJ and Zhang L (eds.) Annual Report Olentangy River Wetland Park, pp. 2328. Columbus, OH: Ohio State University. Note that numbers reflect percent of inputs or outputs. 186 Hydrology _ Wetland Hydrology Glossary Adventitious roots Roots formed above ground; in wetland and aquatic plants they are induced by prolonged inundation. Aerenchyma Air-filled tissue in plants (typically in wetland and aquatic plants) that facilitates air movement from aboveground plant parts to roots. Aufwuchs Plants and animals attached to plants, rocks, pilings, or other erect materials in water. Biologic zero A term used by soil scientists to refer to the temperature threshold that generally causes soil microbes to become relatively inactive, so that reducing conditions do not readily develop in saturated soils; defined by the soil temperature of 5 C or 41 F measured at a depth of 50 cm (20 in.) below the soil surface. Flatwood Low flat, forested landscape typical of coastal or glaciolacustrine plains; soils vary from poorly drained to well drained with slight changes in topography. Flooding In general terms, a condition where an area is inundated (covered by water); soil scientists tend to restrict the term to inundation resulting from overbank flooding of a river or stream. Floodplain Nearly level alluvial land subject to peri- odic inundation (overflow from river or stream). Glaciolacustrine plain Low flat landscape asso- ciated with a former glacial lake, the exposed bed of a former glacial lake. Graminoids Grasses (members of the Family Poaceae true grasses) and grasslike plants (typically members of the families Cyperaceae: sedges, bul- rushes, spikerushes, beakrushes, and cotton-grasses and Juncaceae: rushes, plus other herbaceous plants with long narrow grasslike leaves). Hydraulic conductivity Measure of the ability of water to flow through the soil; low conductivity resists flow, while high conductivity favors flow. Hydric soils Soils formed under frequent and pro- longed reducing conditions due to excessive wet- ness; soils typical of wetlands. Hydrology The scientific study of water properties, distribution, and circulation; also the dynamics of water presence and movement in a particular habi- tat (e.g., wetland hydrology, lake hydrology, or for- est hydrology) or the study of these patterns. Hydrophytic vegetation Plants adapted for life in permanently to periodically flooded or waterlogged substrates; plants growing in water and wetlands. Hypertrophied lenticels Expanded, enlarged corky pores on woody plants typically the result of pro- longed inundation. Isolated wetlands Better referred to as geographi- cally isolated wetlands, wetlands that are sur- rounded by upland (nonhydric soils), with no surface water connection to other wetlands or waters; these wetlands may be connected hydrologi- cally to ground water. Karst terrain A landscape formed in a limestone region where the topography is shaped by dissolu- tion of limestone (or dolomite, gypsum, or salt), characterized by caves, springs, seeps, sinkholes, and disappearing streams. Lenticels Corky roundish pores or lines on bark of woody plants that facilitate gas exchange between inner plant tissue and the atmosphere. Meteoric water Water precipitating from the atmos- phere as rain, snow, sleet, hail, fog, or mist. Morainal deposit Unsorted rocky and soil material (till) carried by and deposited by glaciers, typically marking the extent of glacier advance (terminal moraine) or the sides of the glacier (lateral moraine). Paludified landscape Peat-dominated landscape in regions of high rainfall and low evapotranspiration (often cool, wet climates) formed by the process of paludification where peat mosses (Sphagnum spp.) grow over once dry land converting it to bog (peatland; blanket bogs). Ponding A term mostly used by soil scientists to de- scribe inundation resulting from surface water runoff into a closed depression or water accumulating in a depression from precipitation or high ground water. Porosity The state of having pores or space filled with gases or liquids; also a measure of the volume of pores in a material relative to the total volume of the material; sandy soils have higher porosity (a higher ratio of pore space to a given volume) than clayey or other fine-grained soils. Sink (or sump) From a hydrological standpoint, an area lacking an outflow where water accumulates or is absorbed, including terminal basins associated with watersheds in some arid regions (e.g., the Great Basin of the southwestern United States). Hydrology _ Wetland Hydrology 187 Telluric water Water from the earth, ground water. Throughflow A condition where water both enters and exits an area; water moves through the wetland, for example. Vernal pool A type of open-water wetland where water is present seasonally (spring in temperate regions); vernal pools may be imbedded in woodlands as in the eastern United States or in grasslands as in the western United States (e.g., California, Oregon, and Washington); in Mediterranean climates, these wetlands are typically inundated in winter. Waterlogging A condition where the substrate is saturated at or near the surface for extended peri- ods; in wetlands, saturation is usually long enough to create anaerobic (low oxygen) and reducing soil conditions that affect plant growth. Wetland In general terms, a shallow-water ecosystem or at least, periodically wet ecosystem subject to fre- quent inundation or prolonged soil saturation (water- logging) that is often characterized by hydrophytic vegetation, other aquatic organisms, and hydric soils/substrates; a variety of specific definitions have been created for a host of purposes (legal and scientif- ic) including land use regulation, habitat protection, and natural resource inventories. Wetland hydrology The recurrent, sustained satura- tion of substrates at or near the surface by either surface or ground water sufficient to create condi- tions that support aquatic life including the growth of hydrophytic vegetation, and the formation of hydric soils or substrates; the dynamics of water presence and movement in wetlands. See also: Atmospheric Water and Precipitation; Evapo- transpiration; Ground Water; Hydrological Cycle and Water Budgets. Further Reading Carter V (1996) Wetland hydrology, water quality, and associated functions. In: Fretwell JD, Williams JS, and Redman PJ (eds.) National Water Summary on Wetland Resources, Water-supply paper 2425, pp. 3548. Reston, Virginia, USA: U.S. Geological Survey. Fretwell JD, Williams JS, and Redman PJ (eds.) (1996) National Water Summary on Wetland Resources, water-supply paper 2425. Reston, VA: U.S. Geological Survey. Gilman K (1994) Hydrology and Wetland Conservation. Chichester, England: John Wiley & Sons. Ingram HAP (1983) Hydrology. In: Gore AJP (ed.) Mires: Swamp, Bog, Fen, and Moor. Ecosystems of the World 4A, General Studies, ch. 3, pp. 67158. Amsterdam, The Netherlands: Elsevier Sci- ence. Jackson CR (2007) Wetland hydrology. In: Batzer DP and Sharitz RR (eds.) Ecology of Freshwater and Estuarine Wet- lands, ch. 3, pp. 4381. Berkeley, CA: University of California Press. Mitsch WJ and Gosselink JG (2000) Wetlands. New York, NY: John Wiley & Sons. National Research Council, Committee on Characterization of Wetlands. (1995) Wetlands: Characteristics and Boundaries. Washington, DC: National Academy Press. Price JS, Branfireun BA, Waddington JM, and Devito KJ (2005) Advances in Canadian wetland hydrology, 19992003. Hydro- logical Processes 19: 201214. Richardson JL, Arndt JL, and Montgomery JA (2001) Hydrology of wetland and related soils. In: Richardson JL and Vepraskas MJ (eds.) Wetland Soils: Genesis, Hydrology, Landscapes, and Clas- sification, ch. 3, pp. 3584. Boca Raton, FL: Lewis Publishers. Stone AWand Lindley Stone AJ (1994) Wetlands and Groundwater in the United States. Concord, NH: The American Ground Water Trust. Tiner RW (1999) Wetland Indicators: A Guide to Wetland Identi- fication, Delineation, Classification, and Mapping. Boca Raton, FL: Lewis Publishers, CRC Press. Tiner RW (2005) In Search of Swampland: A Wetland Sourcebook and Field Guide. New Brunswick, NJ: Rutgers University Press. Williams TM (1998) Hydrology. In: Messina MG and Conner WH (eds.) Southern Forested Wetlands: Ecology and Management, pp. 103122. Boca Raton, FL: Lewis Publishers. Winter TC (1989) Hydrologic studies of wetlands in the northern prairie. In: Van der Valk A (ed.) Northern Prairie Wetlands, pp. 1654. Ames, IA: Iowa State University Press. Winter TC and Woo MK (1990) Hydrology of lakes and wetlands. In: Wolman MG and Riggs HC (eds.) Surface Water Hydrology of North America, vol. 1, pp. 159187. Boulder, CO: Geological Society of America. Relevant Websites water_monitor_technote.pdf. 188 Hydrology _ Wetland Hydrology HYDRODYNAMICS AND MIXING IN LAKES, RESERVOIRS, WETLANDS AND RIVERS Contents Biological-Physical Interactions Density Stratification and Stability The Surface Mixed Layer in Lakes and Reservoirs Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) Currents in Rivers Currents in Stratified Water Bodies 1: Density-Driven Flows Currents in Stratified Water Bodies 2: Internal Waves Currents in Stratified Water Bodies 3: Effects of Rotation Currents in the Upper Mixed Layer and in Unstratified Water Bodies Flow in Wetlands and Macrophyte Beds Flow Modification by Submerged Vegetation Hydrodynamical Modeling Biological-Physical Interactions C S Reynolds, Centre of Ecology and Hydrology and Freshwater Biological Association, Cumbria, UK 2009 Elsevier Inc. All rights reserved. Introduction As formal branches of science, limnology and ecology are each around a century in age. Both disciplines feature prominently in the evolving understanding of inland waters, where they are invoked to explain observable phenomena and their role in shaping the abundance, structure, and variability of the biotic communities. It is also true that, from the pioneer studies onwards, much of the scientific investigation has been focused on the mutual relationships among the biota and their chemical environments, most espe- cially with regard to the important nutrient elements. Physical factors were not overlooked altogether: it is well known how the specific heat of water, its curiously variable coefficient of thermal expansion, and its transparency each influence the stability and duration of seasonal thermal stratification or to the underwater distribution of macrophytic plants and photosynthetic algae. The benefit to aquatic organ- isms of the mechanical support contingent upon the high density of water is also generally understood. On the other hand, the mathematics of fluid motion in lakes proved to be less amenable to solution, so its impact on the evolutionary ecology of the pelagic biota those of the open water, mostly living inde- pendently of shores or the bottom oozes for a long time remained wholly intuitive. Although broad pat- terns of wind- and gravity-generated currents could be described and modeled, the smaller scales of water movement and the quantitative description of turbu- lence were, until the last twenty years or so, relatively intransigent to solutions relevant to the function, selection, and evolutionary ecology of aquatic biota, or even to such matters as the transport and dispersal of organisms, particles, and solutes. This chapter reviews briefly the physical properties of fluid motion at the macro and microscale in inland water bodies, seeking to establish the spatial and temporal scales that impinge directly and indirectly on the organisms that live there, as well as on the functional adapta- tions that enable them to do so. Water Movements The Concept of Scale From the major oceanic circulations down to the (Brownian) behavior of the finest colloidal particles and the diffusion of solutes, water characteristi- cally comprises molecules in motion. Curiously, the propensity of water molecules to polymerize into larger aquo complexes, which is responsible for the relatively high density and viscosity of liquid water, makes them resistant to movement, so there is a con- stant battle between, on the one hand, the energy sources driving motion (the Earths rotation, gravita- tional flow, convectional displacement due to thermal expansion and contraction and, especially, the work 189 of wind forcing applied at the water surface of lakes; and, on the other, the resistance of internal viscous forces. Thus, the energy of external forcing is dissipated through a cascade of turbulent eddies of diminishing size and velocity, to the point that it is overwhelmed at the molecular level. Turbulence in the upper water column affects pelagic organisms through several mechanisms operating at a range of temporal and spatial scales. Mixing influences the distribution of regeneration and recycling of dissolved nutrients, the dispersion of zoo- plankton, the location of rewarding feeding grounds for fish, and the resuspension of detrital particles, including biotic propagules. In relation to the depth of light penetration, the penetration of mixing may constrain the exposure of entrained photosynthetic algae and bacteria to light and to regulate their pri- mary production. At the microscale, turbulence is relevant to individual organisms, conditioning their suspension in the mixed layer, the interaction with their own intrinsic motility and the fluxes of dissolved nutrients and gases to their cells. It is to the latter influences that this article is particularly addressed. Small-Scale Turbulence The measurement of turbulence or its convenient components, such as the shear or friction velocity (symbolised as u*), is not the concern of the present chapter. Turbulence in the upper water column is induced by wind, heat loss, and wave breaking. When wind is the predominant cause of turbulence, the turbulent velocity can be approximated from the shear stress at the airwater interface; if convective heat loss is the dominant driver, then a similar turbu- lent velocity scale, w*, comes from the velocity of the resultant convectional plumes; if several processes are operating simultaneously, all are included in the cal- culation, and the resultant turbulent velocity scale is sometimes called the turbulent intensity u. Deeper in the water column, turbulence is often caused by breaking internal waves. Technically, the turbulent intensity is the root mean square velocity of the velocity fluctuations in a turbulent flow field. This measurement has only recently been applied in lim- nological studies. More commonly, turbulence is obtained from microstructure profiling as the rate of dissipation of the turbulent kinetic energy e with the assumption that turbulence production and dissipa- tion are in balance. When turbulence is induced by wind in the surface layer, the turbulent velocity scale is roughly proportional to the square root of the quotient of the applied force per unit area (t, in kg m1 s2 ) and the density of the water (rw, in kg m3 ). Then u tr1 w 1=2 1 The units are in m s1 . The rate of dissipation of turbulent kinetic through the spectrum of eddy sizes (e) is correlated to the dimensions of the largest eddies in the turbulence field (le) and their velocities (u) through eqn. [2]: E u3 l1 e 2 The units are thus m2 s3 . The energy is lost, as heat, through progressively smaller eddies. If the dissipa- tion rate is measured, and the root mean square sizes of turbulent eddies with microstructure profiling, then the turbulent velocity scales are obtained. Even- tually, the spectrum collapses at the point where the driving energy is finally overcome by viscosity: the size of the smallest eddy (lm) is predicted by: lm =rw3 E1=4 3 where Z is the absolute viscosity of the water (units: kg m1 s1 ). These various equations have been used to calculate that the turbulence generated in the open waters of the unstratified Bodensee (Lake of Con- stance) by winds of 520 m s1 drive a spectrum of eddies penetrating to depths of between 45180 m, dissipating at rates (e) of between 1.4 108 to 2.2 107 m2 s3 and culminating in eddy sizes (lm) of between 2.9 and 1.5 mm. In stratified lakes, where the density gradient acts as a barrier to penetration by weak eddies, and in shallow lakes, where the water column is unable to accommodate the unrestricted propagation of turbulence, the same driving energy must be dissipated within a smaller spatial extent and, hence, at a faster rate and to a smaller spatial limit. The energy of a 20 m s1 wind applied to Lough Neagh (mean depth < 9 m), is calculated to be dissi- pated at $4.3 106 m2 s3 , i.e., at nearly twenty times the rate in Bodensee, under the same wind forcing, and culminating in an eddy size of $0.7 mm. In the most aggressively mixed estuaries and fluvial rapids, e may approach 5.5 104 m2 s3 , with eddies as small as 0.2 mm across. The highest values observed in lakes are near the airwater interface and are of order 105 m2 s3 but typical high values are of order 106 m2 s3 . The capacity of turbulent motion to entrain parti- cles, including living organisms, depends broadly upon the magnitude of the relation of the turbulent velocity scale to the intrinsic rates of gravitational settling of the particles in water (ws, in m s1 ). Whereas a stone always drops almost unimpeded through water, parti- cles of clay ( 0, turbu- lence lifts relatively heavy fluid particles up; in this case, Jb is negative, representing a loss of energy by the turbu- lence. This is the case whenturbulenceis mixing a stably stratified fluid. The opposite case is found when the surface of the lake is cooled, leading to convection. Here w0 < 0 and r0 > 0, meaning that relatively heavy fluid particles are falling through the fluid, generating turbulence; in this case, B is positive, representing a gain of energy by the turbulence. Finally when turbulence is inhomogeneous, i.e., varies spatially, as is the case in the SML, there can be redistribution of turbulent kinetic energy by the turbulence. This is accomplished by pressure-velocity correlations (like in a engine cylinder!) and by triple correlations of fluctuating velocities. While the details of redistribution are more obscure, what is observed is that the transfer term, T, acts to move TKE from high turbulence regions to low turbulence regions. Thus, the final accounting for TKE for a one- dimensional water column as we will describe below reads: @ TKE @t P Jb e @T @z 6 This relation is fundamental to lake turbulence dynamics; in what follows, we will emphasize its use in understanding the dynamics of and modeling the SML. Winds on Lakes When wind blows over the lake surface it applies a force, i.e., imparts momentum, to the fluid, driving mean currents, generating surface waves, and produc- ing turbulence, either through instability of the shear flow created by the wind or through wave breaking (Figure 2). In terms of U10, this force, represented as a stress (force/area) is given as t0 raCDU2 10 ru2 7 Wind Heating and cooling Surface (diurnal) mixed layer Diurnal thermocline (entrainment interface) Seasonal thermocline Hypolimnion Layer Lake bottom Water surface = Turbulent (wind/convection) Intermittently turbulent (shear) Mostly laminar Turbulence state Temperature () z hm z Figure 1 Sketch of lake thermal structure showing the surface mixed layer as well as layers below. 208 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs where ra is the air density, CD O 103 is the drag coefficient, U10 is the wind speed measured at 10 m above the lake surface, r is the water density, and u is the shear velocity in the water. Besides atmospheric stability, for lakes, CD can depend on fetch (the dis- tance over which wind-generated waves propagate), especially including topographic sheltering by sur- rounding hills or even trees in the case of small lakes, and on wind speed. The transfer of momentum from the wind to the water at the air-water interface depends on how the airflow over wind-generated surface waves is modi- fied by the presence of those waves, a modification that depends both on the height of the waves and their wavelength. These two features of surface waves increase with increasing fetch. Consequently, CD depends on fetch and wind speed. The drag relation, eqn. [7], represents the total momentum input from the wind. However, only part of it goes directly into the underlying flow; the rest goes to making the waves grow. This wave stress can be 50% of the total stress. Ultimately, the waves reach a state wherein the rate of input from the wind is matched by the loss of momen- tum to the mean flow by wave breaking, a state in which all of the wind stress is applied to the mean flow. Practically, given the fact that the winds often vary considerably over the surface of a lake, and that often even in the best of circumstances, only one wind station might be available on the lake, it often suffices to assume that CD % 1:3 103 . The shear velocity in the water, u, plays a central role in representing flows in the SML. In many cases the mean velocity has been found to vary logarithmically with distance, z0 , measured down from the water surface, i.e., the difference between the velocity at the water surface, Us, and at any depth satisfies the well established law of the wall that describes flows in turbulent boundary layers: U ! z0 Us u k ln z0 z0 8 where k 0:41 is the von Karman constant, and z0 is the apparent roughness of the near surface flow. Most studies have found that z0 is proportional to the sur- face wave height albeit much smaller. Given the com- plex physics operant at the air-water interface, it is hardly surprising that the reasons for this behavior remain unclear. Although difficult to measure, labo- ratory and field observations suggest Us % 25u. The law of the wall description is useful in that it has well- known properties, e.g., the eddy viscosity and thus eddy diffusivity (the mixing coefficient for scalars like dissolved oxygen) vary parabolically within the SML and are proportional to u: nt kuz0 1 z0 hm 9 The dependence of nt on u comes about because the turbulent velocity scale q $ u, whereas the turbu- lence length scale, which varies with position within the SML, is proportional to hm but depends on posi- tion within the mixed layer. From the standpoint of TKE dynamics, near the water surface, P and e are in balance, and since u0w0 u2 is nearly constant: e % P u3 kz0 10 Stress WASL + SBL SBL Wave u(z) Net heat flux Wave breaking Stokes drift Thermocline z Convection Langmuir circulationLog-layer Figure 2 Sketch of SML including waves, Langmuir circulations etc. (Figure 2 in Wuest and Lorke used with permission.) WASL refers to the wave affected surface layer, i.e., the region in which enhanced turbulence due to breaking is important. Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs 209 However, observations of the SML show that it dif- fers from simpler boundary layers in two important ways. First, the presence of waves brings into play two phenomenon not found in canonical law of the wall flows: wave-breaking, an extra source of TKE near the surface; and Langmuir cells or circulations (LCs), large-scale, streamwise vortices thought to be produced by wave-current interactions. Secondly free-convection due to surface cooling can also intro- duce TKE into the SML. Furthermore, continued heating of the upper water column can modify the energy balance above such that some of the energy introduced into the SML is lost in working against buoyancy forces. Modifications to the predicted law of the wall scaling are described in eqns. [15] and [16]. When surface waves break they transfer momen- tum and energy into the underlying flow. In terms of turbulence dynamics, this can be viewed as providing, an extra source of TKE near the surface that diffuses down into the underlying flow such that the TKE balance changes to one in which e % @T=@z. Empiri- cally, it is found that the flux of TKE from the water surface, i.e., the breaking region, is 60100 u3 , which gives rise to values of e much larger than those pre- dicted by eqn. [10]. The thickness of this layer of enhanced e is O u2 =g ; inside this layer e decays rap- idly, i.e., e / z03 . Nonetheless, below this region, e tends to wall values. Because of this behavior, it appears that wave-breaking is a critical aspect of air-water gas exchange and near-surface turbulence but may not be important to processes at work deeper in the SML such as those responsible for deepening of the SML. Besides injecting turbulence into the SML by break- ing, surface waves also modify horizontal transport because of their associated Stokes drift velocity, U ! Stokes, the difference between mean Lagrangian velocity of water particles (i.e., the average velocity of particular particles) and the mean Eulerian velocity (i.e., the average measured at fixed points). As discov- ered by Stokes in 1848, U ! Stokes comes about because even though the wave motion at any point may have zero mean (as is this case with surface waves), as fluid particles move under the waves, they sample the velo- cities of points in the fluid that are slightly different from the velocity where they started, resulting in drift in the direction the waves are moving. Written for waves with wavelength that is short relative to the SML depth, i.e., l 2p k k ! k < hm, where l is the surface wave wavelength and k ! is the wavenum- ber vector, the Stokes drift velocity is U ! Stokes ak 2 exp 2kz C ! p U 0 Stokesexp 2kz C ! p k C ! pk 11 for wave height a and phase velocity C ! p 2pg Tw k ! k k ! k 12 Here Tw is the wave period. In addition to its importance to the horizontal trans- port of floating materials, waves, through the Stokes drift also can drive LCs, aka windrows, arrays of streamwise vortices roughly aligned with the wind that collect floating materials (foam, garbage, jelly- fish. . .) at their convergences on the surface (Figure 3). As first revealed in studies by the chemist Irving Lang- muir made in Lake George, New York, LCs can have a profound effect on the overall flow in the SML; in particular they can rapidly transport neutrally buoyant materials, e.g., phytoplankton cells, to the base of the SML. Current theory views LCs as being driven by the averaged interaction of surface waves with the mean flow. This interaction leads to an extra net force on the mean flow referred to as the Craik-Leibovich force (after the theorys developers) that is the cross product of the Stokes drift velocity and the mean vorticity of the flow. Analysis of the stability of flows driven by wind stresses in the presence of Stokes drift, shows that when @ U ! Stokes @z @ U ! @z > 0, LCs can develop. This condition is generally satisfied in lakes since both the waves and wind and wind-driven flow tend to be co-aligned. While LCs can exhibit complex pairing and branching behavior (Figure 3), and some substan- tial unsteadiness, generally the end state of the insta- bility is a set of rolls that have a dominant wavelength across the wind that is twice the SML depth, and Figure 3 Langmuir circulations visualized by flotsam lines on the Great Salt Lake, Utah (USA). Photo taken from a small airplane by Dr. Steve Robinson. The main row spacing is comparable to the depth. Used by permission. 210 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs produce a velocity in the plane perpendicular to the wind uLC $ O U0 s u that can be several cm/s, result- ing in relatively rapid stirring of the upper mixed layer. Recent numerical studies of turbulent LCs make use of the fact that the Craik-Leibovich force also describes the interactions of waves with low- frequency turbulence, suggesting that LCs can be considered to be an organized form of turbulence. Questions about the role of LCs in SML dynamics remain: For example, given that LCs can transport significant momentum downwards, it is conceivable (although not yet shown observationally) that they may dominate the downwards transport of horizon- tal momentum, thus altering the fundamental physi- cal basis of the law of the wall velocity profile discussed above. Moreover, it is clear that LCs in shallow flows over a solid, no-slip bottom seem to be more stable and more clearly defined than those in the SML (see Figure 3), which, in effect, overlies a slippery bottom. Besides waves, the SML also differs from the gene- ric wall layer in that there are significant heat and thus buoyancy fluxes through the airsea inter- face. When cooled from the surface, the SML will experience free convection; the surface of the lake will be 0.01 C 0.1 C or so cooler than the water immediately beneath leading to gravitational instabil- ities with parcels of fluid intermittently breaking away from the free surface and dropping through the SML to the base of the SML. By continuity, these plumes must be matched by upward rising fluid elements at the same time. For a surface buoyancy flux Jb0 ag eH rcp 13 where eH is the surface heat flux (positive outwards for cooling) and cp is the heat capacity (4.2 103 J C1 kg1 ), the characteristic velocity of these plumes (assuming that Jb0 > 0) is uf Jb0hm 1=3 14 Thus, in the presence of cooling, wind stress and surface waves, there are potentially 3 velocity scales for turbu- lent motions in the SML, u, uLC , and uf . With both buoyancy and shear (but omitting wave effects), the lacustrine SML bears a strong similarity to the atmospheric boundary layer, where both buoy- ancy and shear can be important. In this case, a second length scale in addition to the mixed layer depth comes into play: the Monin Obukhov length, LMO u3 kJb0 15 a length scale that characterizes the importance of the buoyancy flux relative to the wind stress (or equivalently in the absence of Langmuir circulations) the near surface shear. When LMO > 0, the equilib- rium SML depth produced by mixing in the presence of a stabilizing buoyancy flux will be LMO. When LMO < 0, LMO is the depth at which buoyancy effects equal shear effects. Indeed, careful measurements of e made in lake SMLs match the depth variation observed in atmospheric flows, i.e., ekz0 u3 1:14 1 0:46 z0 = LMOj j 2=3 3=2 16 Note that for small values of z= LMOj j, eqn. [16] reverts to the law of the wall whereas the dissipation associated with convective plumes tends to be nearly independent of depth and approximately equal to Jb0. Although there are no suitable measurements that show this behavior, one can imagine that cooling with wave breaking should lead to a three layer structure a near surface wave layer with very high values of e, a law of the wall layer and a deeper convective layer, the latter two described by eqn. [16]. Of course, convection also modifies the shear flow, with the enhanced vertical mixing reducing the vertical shear, while for small stabilizing buoyancy fluxes the vertical shear is enhanced, behaviour that has been found for the atmospheric case to be represented by a modified law of the wall. Surface Energy Exchanges Heat fluxes through the air-water interface are due to net shortwave radiation (Qsw), net longwave radia- tion (Qlw), latent heat transfer (Hl) and sensible heat transfer (Hs). The total surface heat exchange can be written as eH Qsw Qlw Hl Hs 17 where the usual sign convention is that eH is negative for heating of the water column and positive for cooling. The downward shortwave radiation Qsw is usually measured directly, and the upward component due to reflection is either measured directly or accounted for by a calculation based on the variation of albedo with sun angle. Unlike the other components of the surface heat flux, Qsw penetrates into the water column according to Beers law: Qsw z Qsw 0 exp bz 18 where b1 is the effective extinction depth for light. Often eqn. [18] is modified to be the sum of terms reflecting different extinction lengths for different portions of the irradiance spectrum. The diffuse atten- uation coefficient measured in the visible part of the spectrum, bd, depends on what is in the water column, Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs 211 e.g., fine sediment particles, dissolved organic matter, or phytoplankton; consequently it varies daily, weekly, seasonally, and inter-annually in response to changing sediment inputs and chemistry and biology of the lake. Qsw acts to stratify a water column except when water temperatures are below the temperature of maximum density. The net long-wave radiation Qlw is the difference between incoming infrared radiation from the sky and outgoing infrared radiation from the water sur- face. These values can be measured directly but in the absence of instrumentation, the net heat loss from the lake can be calculated from observations of air tem- perature, lake surface temperature and cloud cover using any one of a number of formulations. One popular model for Qlw is: Qlw 5:23 108 Ts 4 5:18 1013 T6 a 1 0:2C2 19 where Ts is the water surface temperature ( K), Ta is the atmospheric temperature ( K)(where the height of measurement depends on the thickness of the atmo- spheric boundary layer; typically 10 m for large lakes and 23 m for small), and C is the fraction of sky covered with clouds. The dependence on clouds is the result of blackbody radiation by water moisture in the atmosphere. The coefficients include emissivity of air, which is proportional to Ta 2 , and water as well as Stefan Boltzman constant. The latent heat flux, Hl is the surface heat loss due to evaporation. Hl is parameterized in terms of air density, ra, latent heat of evaporation, Lw, the wind speed U10 and relative humidity, r, both measured at 10 m, and the saturation humidity at the water sur- face temperature, qs Ts Hl raLwClU10 qs q r; Ta 20 The exchange coefficient Cl % 0:0015 is an empirical function of fetch and atmospheric stability. In a like fashion, the sensible heat flux is given as Hs rcpCsU10 Ts Ta 21 where Cs % Cl is also an empirical constant. Given the surface heat fluxes, the first law of ther- modynamics describes the subsequent evolution of the temperature field. Written for a one-dimensional water column, this reads: @Y @t 1 rcp @Qsw @z @ w0y0 @z 22 where the surface value of the turbulent heat flux is equal to the total surface heat flux minus the short wave radiation, i.e.: w0y0 j0 HLW HL HS 23 It is the vertical variation in shortwave radiation that creates stratification, hence the extinction scale b1 plays a fundamental role in determining SML depth. An example of time series of surface meteorology, the resulting energy fluxes at the air-water interface, and the sum of the surface energy fluxes and the effective heat flux are presented in Figure 4 for a small arctic lake during summer. The resulting evolu- tion of the thermal structure is illustrated in Figure 5. The forcing of the surface layer during periods with warm and cold fronts differs considerably with con- sequences for thermal structure. During cold fronts, clouds are prevalent and reduce the short wave inputs, air temperatures drop below surface water temperatures thus setting the stage for increases in sensible heat losses, and relative humidity increases. Winds came up during the second half of the cold front illustrated here, day of year (doy) 210215 such that sensible and latent heat fluxes both increased with total heat loss of 400 W m2 . Due to the high cloud cover, the sum of the terms in eqn. [24] is positive for only brief periods during the day and overall the lake loses heat. In contrast, when warm air masses are present, cloud cover is lower, air tem- peratures diurnally increase and decrease to tempera- tures just above and just below surface water temperatures, and winds often have a diel periodicity. In consequence, the terms in eqn. [24] vary from negative in the day (the lake is gaining heat) to posi- tive at night (the lake loses heat). The consequences of these variations in surface forcing are readily observed in the lake thermal structure. During peri- ods with warm air masses, the upper layer heats on a daily basis and a diurnal thermocline forms. In con- trast, during the initial part of a cold front when winds were light, day 210212, the surface layer slowly loses heat. Temperatures decrease much more rapidly as the heat losses increase and the mixed layer deepens from 3 to 6 m. On a global scale, latent heat fluxes tend to domi- nate cooling from the tropics to the poles although net longwave radiation can be significant particularly on cloud free nights. Sensible heat fluxes can either heat or cool but are generally smaller than the other terms. Experience has shown that given a weather station located on the lake that measures wind- speed, relative humidity, air temperature, and inci- dent solar radiation, the above relations are likely accurate to 1020 W m2 . The intensity of turbulence and the size of turbulent eddies over a diurnal period with light wind forcing are illustrated in Figure 6. Heat loss at night, accompanied by light breezes, generates eddies which fill the SML and turbulence is measured throughout. During the day, due to posi- tive effective heat flux, the turbulence is damped at 212 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs depths below a shallow surface layer. Light afternoon winds only tend to cause mixing in a small portion of the SML. Nocturnal cooling again energizes the full SML. During a cloudy, windy period, the SML would remain turbulent throughout the day. Mixed Layer Deepening and Entrainment Mixing and Turbulence Energetics It is the combination of wind stress, convection and surface heating that leads to the formation of the SML and partially sets its depth hm. Qualitatively this can be viewed as follows: energy for mixing (TKE) is introduced at the surface and is partially (or mostly) dissipated within the SML; what remains at the mixed layer base is available to lift colder, heavier fluid up into the mixed layer, thus increasing the potential energy of the water column. The sketch of the SML shown in Figure 7 shows an additional aspect of the problem: besides a near-discontinuity in temperature, there is also a strong velocity shear across the mixed layer base. This shear, which arises from the direct effect of the wind and from seiching in the lake (refer see also section), has two conse- quences: (1) it results in the additional production of TKE at the mixed layer base, and (2) it leads to Kelvin Helmholtz billowing. The consequences for turbu- lence at the base of the mixed layer can be seen in late afternoon in Figure 6. Most current models of 0 200 400 600 800 205 degC% 25 100 50 10 5 200 800 400 400 800 0 100 100 0 0 0 15 5 5 210 215 Shortwave radiation Air and surface temperatures Relative humidity Wind speed Surface heat fluxes Net heat fluxes Day of year 220 225 205 210 215 220 225 205 210 215 220 225 205 210 215 220 225 205 210 215 220 225 205 210 215 220 225 Wm2 ms1 Wm2 Wm2 (a) (b) (c) (d) (e) (f) Figure 4 Meteorological forcing of Lake E5, an arctic kettle lake, from mid-June through mid-August 2004: (a) net shortwave radiation; (b) Air (blue) and surface water (red) temperatures; (c) relative humidity; (d) wind speed; (e) surface heat fluxes comprised of sensible heat flux (blue), latent heat flux (red) and net longwave heat flux (green); and (f) sum of the surface heat fluxes (blue) and total heat flux (green) computed as the sum of surface heat fluxes and net short wave absorbed in the surface mixing layer. (MacIntyre S, unpublished data). Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs 213 SML dynamics incorporate these ideas through inte- gration of the TKE balance over the entire SML depth in order to arrive at a prediction of the rate of deep- ening of the mixed layer for given forcing. This is also known as the entrainment velocity. While the details of the integration are complicated, the result can be represented as a simple energy balance: g0 hm 2 dhm dt CF 2 E3=2 s CsDU2 2 dhm dt Es 2 dhm dt 24 where g0 gDr=r0 is the effective gravity associated with the density jump Dr across the mixed layer base. The LHS of eqn. [24] is the rate of change of potential energy, i.e., the rate at which work must be done to lift heavy fluid from the base of the mixed layer up to the centroid of the SML. The terms on the RHS represent respectively the flux of TKE from the surface that is available for mixing, the generation of TKE in the interface by shear, and the rate at which energy must be added to make entrained fluid turbulent. Aside from the constant, the formula- tion of mixed layer shear production is exact in that when a slower fluid from below the mixed layer is entrained there is a loss of mean kinetic energy. Turbulence in the SML is parameterized by the combination of turbulence associated with the wind and cooling: Es 1 CE CF 2=3 u3 f C3 Nu3 2=3 25 The constants in eqns. [24] and [25] reflect efficien- cies of mixing, e.g., only a small fraction of the TKE introduced to the SML ends up increasing the poten- tial energy of the fluid. As determined from labora- tory, numerical and field experiments, they are given in Table 1. While eqn. [24] is relatively complete, it includes simpler, limiting cases such as the slow deepening of the mixed layer due to wind stresses when DU and uf are negligible: dhm dt CFE3=2 s g0hm CFC3 N CE CF u3 g0hm 0:42 u Ri 26 The inclusion of interfacial shear production, which has much higher efficiency because it takes place in the entrainment interface, gives an entrainment law, a relation between mixed layer parameters and deepen- ing rate that depends on shear as is often observed in laboratory experiments. An interesting limit is one in 102 101 LN 100 Depth[m]Depth[m] 2 2 4 6 4 6 8 205 210 215 Day of year Log10(Eddy Diffusivity) 220 20 15 10 C 5 2 4 6 205 210 215 220 225 225 8/017/25(a) (b) (c) 8/08 Figure 5 Time series of (a) Lake Number, (b) thermal structure as 0.5 C isotherms, and (c) coefficient of eddy diffusivity at Lake E5, Alaska, from mid-June through mid-August 2004. The coefficient of eddy diffusivity Kz (m2 s1 ) is computed for the SML as the product of c1q* l where q* is obtained from the turbulent velocity scales for heat loss and wind shear in eqn. [25], l is the size of the energy containing eddies here defined as the depth of the actively mixing layer and c1 is estimated as 0.1. Below the SML, Kz is estimated as from a heat budget method. Depths where assumptions for calculations were not met are white. (MacIntyre S, unpublished data) 214 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs which shear dominates; in this case, the mixed layer depth is set by a stability condition similar to (1): hm Cs DU2 g0 27 In contrast to the stirring limit, eqn. [27] implies a strong coupling between mixed layer motions and deepening, e.g., showing that the entrainment law depends on the rate at which the shear changes in time. In lakes, shear and wind stirring are not indepen- dent. While the details depend on lake geometry and stratification, and the importance of rotation, the simple model of a two-layered lake with constant depth and a suddenly imposed wind provides a good basis for understanding when and how shear can be important. In this case, the velocity shear builds linearly in time until the effects of the edges of the lake are felt, cutting off the shear. Analysis of this case shows that the importance of shear production to entrainment can be assessed using a parameter known as the Wedderburn number: W g0 h2 m u2 L 28 where L is the length of the lake. When W < 1, shear production is important and deepening, whereas as W is increased above 10, shear production becomes less and less important and deepening is slower (Figure 8). Mixed layer shear also brings into play the shearing instability known as the Kelvin Helmholtz instability, with its distinctive spiral eddying motion, Kelvin Helmholtz (KH) billows (Figure 9). KH billows 06:00(a) (b) (c) Depth[m] 0 25 20 15 10 5 Depth[m] 0 25 20 15 10 5 Depth[m] 0 25 20 15 10 5 09:00 12:00 15:00 18:00 18 16 14 C 12 6 4 3 2 1 0 7 8 9 10 11 06:00 09:00 12:00 15:00 18:00 log(m2 s3 ) 06:00 09:00 12:00 Time of day 15:00 18:00 LC(m) Figure 6 Time series of (a) temperature, (b) rate of dissipation of turbulent kinetic energy (e), and (c) size of turbulent eddies in Lake Tahoe, CA in Sept. 2001. Data were obtained with a SCAMP microstructure profiler ( Winds were light (0.25. Empirically, this can be represented by the simple prescription: billowing of a sheared interface will lead to a stable interface thickness ds 0:3 DU2 g0 29 Arguably one of the most accurate rules applying to stratified turbulence, when applied to the two layer lake with W $ 1, eqn. [29] predicts that besides rapid deepening of the mixed layer, mixed layer shear will lead to billowing that can give interface thicknesses that occupy a large fraction of the water column. Upwelling Given that the steady slope of the interface under the action of the wind is O u2 =g0 hm (refer see also section), W also measures the upwind displacement of the interface relative to the at-rest mixed layer thick- ness. Thus, when W $ 1, the interface should surface at the upwind end of the lake, i.e., there will be upwelling (Figure 10). This is important because upwelling funda- mentally changes how mixing takes place. In the absence of upwelling, entrainment at the mixed layer base does not affect the fluid below. In contrast, during upwelling, fluid from below the mixed layer is mixed with water in SML, creating intermediate density fluid. While upwelling is underway, the steady wind-driven flow disperses the upwelled fluid downwind, in a pro- cess, once described as edge leakage, that is formally analogous to shear-flow dispersion. At this time, hori- zontal density gradients develop in the SML. When the wind ceases, gravity induces this layered fluid to flow as intrusions into the thermocline resulting in a thickening rather than a sharpening of the thermocline. This behavior would not have been predicted solely on the basis of a one-dimensional model of the lake. Finally, while the two-layer model requires relatively strong winds to create upwelling, in reality since the stratification in lakes is continuous not layered, upwell- ing from within the thermocline, rather than from the hypolimnion is relatively common. A second more general number, one that is based on the actual stratifi- cation and lake hypsography, rather than an assumed layered distribution and constant depth, has been termed the Lake number (usually written as LN),: LN gSt 1 zT zm ru2 A 3=2 0 1 zg zm 30 where zT is the thermocline depth, zM is the maximum depth, zg is the depth of the center of volume, A0 is the surface area, and St zm 0 z zg A z r z dz 31 Qsw 2b1 Turbulent mixed layer Entrainment interface Shortwave radiation Temperature () (qsw) KH billows Velocity (U) Log layer 25u* z hm Hl, Hlw, Hs U ds 0=ru2 * z Figure 7 Sketch of SML showing turbulence dynamics for mixed layer deepening Adapted from Spigel RH, Imberger J, and Rayner KN (1986) Modeling the diurnal mixed layer Limnology and Oceanography 31: 533556. Table 1 Constants in the mixed layer model (after Imberger, 1985) Constant CE CF CN CS Estimated value 1.33 0.25 1.33 0.24 216 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs is the Schmidt stability of the lake. Note that in general, zT 6 hm, since the main thermocline may be deeper than the diurnal thermocline where active entrainment takes place. By analogy to W, when LN < 1, upwelling comes from the hypolimnion, while even for LN up to $10, some form of upwelling is important, i.e., mixing by upwelling is important to overall stratification and SML dynamics. A time series of LN illustrates the dynamic nature of this variable over the stratified period. When it drops to values near 1, the increased shear in the metalimnion is indicated by increases in coefficient of eddy diffusivity, a term indicative of the turbulence in lakes and oceans, in the top of the metalimnion as well as deeper in the water column (Figure 5). The accompanying deepening of the SML and diurnal thermocline, particularly that during the heating period from days 218223, illustrates the enhanced shear when LN is order 1. Synthesis Overall, this process-based view of SML dynamics can be used to explain both diurnal, seasonal, and latitudinal variations in SML depth and stratification in lakes (refer see also section). In small sheltered temperate lakes the conceptual model is as follows: During the spring warming, the lake stratifies, with possible episodes of complete mixing and low LN. As the stratification strengthens through summer, LN tends to be larger (>10) and mixing is driven more by stirring and convection at night. In cases where a shallow diurnal SML develops over a deeper seasonal thermocline, deepening of the diurnal SML can be Figure 9 Kelvin Helmholtz billows created in a two-layer laboratory shear flow. The upper layer is moving to the left whereas the lower (denser) layer is moving to the right. Time increases going from the first panel to the fourth and the sequence shows the build up, roll over, and finally the turbulent mixing of the billows. Photos by Prof. W. Debler; used by permission. U U U U W > 10 2 < W < 10 W ~ 1 W < < 1 No shear Shear Shear Complete mixing Eddies Ri>0.25 Kz, molecular Ri < 0.25 occasionally Kz > molecular Ri < 0.25 more frequently Kz > 10 to 100 molecular diffusivity Thermocline Wedderburn number and thermocline tilting Thermocline, before wind Thermocline tilt from wind Figure 8 Tilting of the thermocline as a function of Wedderburn number or related Lake number and anticipated changes in Ri and measured changes in metalimnetic Kz (Conceptualization developed from Spigel and Imberger (1980) and Monismith (1986) and changes in Kz based on observations from numerous field experiments). Adapted and used with permission from MacIntyre S (2008) Describing fluxes in lakes using temperature arrays and surface meteorology. Verh. Internat. Verein. Limnol. 30(3). Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs 217 driven by shear and heat loss particularly from evap- oration, at least until the SML base reaches the main thermocline. For larger lakes and small unsheltered lakes, the summer stratified period includes multiple episodes with low LN. These commonly occur during the passage of cold fronts, so mixed layer deepening can be rapid due to both shear and heat loss (Figures 5 and 6). In fall, cooling will deepen the mixed layer, but events with LN < 1 will lead to more rapid homogenization. An important aspect of both stirring and shearing is that the overall buoyancy of the SML (g0 hm) never decreases and generally increases as the mixed layer gets deeper. Thus, as the mixed layer deepens due to mechanical forcing, the interface itself becomes more stable. Since billowing spreads the interface, it can work hand in hand with stirring to produce a more rapid deepening of the SML than might be achieved by stirring alone. On the other hand, cooling that drives convection, also weakens the buoyancy in the mixed layer and thermocline; as cooling-driven deepening proceeds, the interface becomes less stable, thus accelerating mixed layer deepening. This process occurs in the night during summer and year round in 0 SB30 SB25 SB20 SB10 SB00 C10 2 4 6 8 10 12 0 26.25 26.00 25.50 25.00 24.75 24.25 23.75 23.50 22.75 (a) (b) Depth(m) 200 Distance (m) Upwelling region Shear stress d r1 T h Streamlines of upwelling flow Isopycnals Velocity profile x=Lx=0 400 600 800 20 u* 2 u* 1000 Figure 10 (a) Temperature structure during upwelling in Wellington Reservoir, Feb 1985 figure taken from Monismith et al. (1990) used with permission by ASLO. In this case the wind is blowing from the right to the left of the picture. The small triangles mark the locations of CTD casts from which the contoured temperature field was produced. (b) Conceptual model of circulation and mixing due to upwelling figure taken from Imberger J and Monismith SG (1986) Appendix to Monismith (1986). Again, isotherms are shown, but in this case the wind stress is in the opposite direction from what is shown in a. 218 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs the tropics. For temperate lakes, it occurs to an even larger extent during the passage of cold fronts during the stratified period, and during fall cooling. The connection of mixed layer shear and mixing offers a dynamical explanation of why larger lakes tend to have deeper mixed layers than smaller ones if exposed to the same wind stress: they are more likely to have small values of LN and thus to experience greater rates of mixed layer deepening in response to wind forcing. However, addressing this problem cor- rectly is complicated and the mixed layer depth of large lakes is likely to be deeper than predicted based on dynamical arguments alone. Small lakes are shel- tered by trees and thus have much reduced fetch. In addition, wind speeds in the center portions of large lakes are much larger than over adjacent land and evaporation rates will also be higher in large lakes. Thus, while the SML will be deeper in larger lakes in the same region, it may be even deeper than predicted based on calculations of Lake number (Figure 11). It is important to note that this classification only applies to lakes that are smaller in horizontal dimen- sion that the first-mode baroclinic Rossby radius, something that is typically the order of 10 km. For larger lakes, the picture is more complicated since the nearshore and offshore regions behave somewhat differently (refer see also section). In the middle of large lakes, mixed layer shear is limited by Coriolis forces rather than by boundary effects such that the response of the lake to starting or stopping the wind is to generate inertial oscillations rather than seiches. However, other mixed layer processes, e.g., LCs, wave breaking, etc. appear to be identical. Understanding the dynamical implications of W and LN is also important for differentiating mixing dynamics in lakes of the same size across latitudinal gradients (refer see also section). For instance, small temperate lakes such as Lawrence Lake, MI (45 420 N, 84 520 W), have W and LN > 100 throughout the summer stratified period. Thus, all the mixing in the 5 10 15 Day of year-1995 Depth(m) 170 Green (0.89 km2 ) Trout 347 km2 Musclow (22.2 km2 ) 180 s 190 Isotherm displacements - NOLSS Lakes 200 210 220 160 160 170 180 190 200 210 220 160 170 180 190 200 210 220 25 20 15 10 5 25 20 15 C 10 5 25 20 15 10 5 5 10 15 20 5 10 15 20 Figure 11 Thermal structure in a set of nearby lakes located in Ontario but having different surface areas. The small lakes are stratified to the surface, the moderate sized lake has a shallow mixed layer except when wind forcing increases for brief periods, and the depth of the SML in large lake is highly variable owing to wind forcing, higher evaporation rates, and the oscillations of internal waves. The onset of stratification was also delayed in the larger lake. Adapted from Kratz TK MacIntyre S, and Webster KE (2005) Causes and consequences of spatial heterogeneity in lakes. In: Lovett GM, Jones CG, Turner MG, and Weathers KC (eds.). Ecosystem Function in Heterogeneous Landscapes. pp. 329347. Springer, NY, used by permission. Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs 219 0 10 20 30 Depth(m) 40 50 60 70 80 5 10 15 20 Temperature (deg C) 25 30 35 40 45 Jan 22 Feb 21 Mar 21 Apr 22 May 20 Jun 17 Jul 15 Aug 11 Sep 12 Oct 14 Nov 18 Dec 16 Figure 12 Annual variation of temperatures in Lake Biwa (S. Endoh, unpublished data). Taken from jp/~endoh/doc/endoh.htm and used by permission. Each profile is progressively offset by 2 C. 0 2 4 6 Depth(m) 8 10 12 29 30 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 31 Temperature (deg C) 32 33 34 35 36 Figure 13 Daily variation in a tropical lake: Kranji Reservoir Singapore March 2324, 2006 (Hench J, Monismith S, Xing Z, and Lo E, unpublished data). The numbers refer to which cast a given profile corresponds. The profiles shown are about an hour apart, with each profile shifted horizontally 0.2 h1 relative to the first profile, which was taken at ca. 1300 hours. The variation seen above for one day is comparable to what is seen over the entire year for Kranji Reservoir. The squiggle seen in many profiles are symptomatic of active turbulent mixing. Note that a uniform, clearly defined SML is only evident in some of the profiles. 220 Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs mixed layer is caused by stirring and heat loss and deepening is dominated by heat loss. In contrast, similar sized lakes in the arctic frequently experience events with LN $ 1 (Figure 5). In such lakes, mixed layer deepening is driven by the combination of heat loss and shear and deeper mixed layers may result. Furthermore, evaporation is larger in warmer water bodies exposed to the same wind forcing. Hence, we predict that mixed layer depth will be deeper in the tropics than the temperate zone for lakes of similar sizes and light penetration, although this effect may be offset by the fact that the thermal expansivity is considerably larger for tropical lake temperatures which can often be in the range 25 C 30 C than it is for colder, higher latitude lakes. The case of LN 1 is particularly relevant to shal- low, polymictic lakes where strong stratification does not develop. Besides shallow lakes, lakes in the tro- pics less than 100 m deep tend to have weak stratifi- cation in the morning and low LN because annual variations in heating and cooling are often minimal compared with the diurnal variation in forcing. That is, the cold water found in the hypolimnion of a temperate lake is not present in a tropical lake, and the annual variations in stratification seen in the tem- perate zone (Figure 12) may occur over the course of a day in the tropics (Figure 13). Thus, the dynamical balances of heating, cooling, wind mixing, and shear vary with lake size, latitude and by season thus creat- ing large but predictable differences in turbulence and the habitat of organisms. Summary The SML of lakes and reservoirs is a dynamic region in which wind, wave, and cooling produced turbu- lence competes with the stabilizing effects of short- wave radiation to determine mixing characteristics and rates of mixed layer deepening. It is generally much more energetic than most of the rest of the lake. Flows in the SML seem to follow scaling laws that parallel those found for turbulent wall flows, particularly those that apply to the atmospheric boundary layer, although there is the added compli- cation that Langmuir cells, large-scale organized structures not generally found in atmospheric or engi- neering flows, may be important. In addition, mixed layer dynamics must take into account cooling at the airwater interface. Finally, while the traditional model of the SML and of lake stratification is a one-dimensional view, i.e., temperatures etc. only vary vertically, it is clear that during strong wind events, horizontal variability can become significant, especially in the case of upwelling. See also: The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs); Currents in Stratified Water Bodies 1: Density-Driven Flows; Currents in Stratified Water Bodies 2: Internal Waves; Currents in Stratified Water Bodies 3: Effects of Rotation; Currents in the Upper Mixed Layer and in Unstratified Water Bodies; Density Stratification and Stability; Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes. Further Reading Anis A and Singhal G (2006) Mixing in the surface boundary layer of a tropical freshwater reservoir. Journal of Marine Systems 63: 225243. Carmack EC and Farmer DM (1982) Cooling processes in deep temperate lakes: A review with examples from two lakes in British Columbia. Journal of Marine Systems 40: 85111. Dillon TM and Powell TM (1979) Observations of a surface mixed layer. Deep Sea Research 26A: 915932. Fischer HB, List EJ, Koh RCY, Imberger J, and Brooks NH (1979) Mixing in Inland and Coastal Waters, 483 pp. San Diego: Aca- demic Press. Gal G, Imberger J, Zohary T, Antenucci J, Anis A, and Rosenburg T (2003) Simulating the thermal dynamics of Lake Kinneret. Ecological Modelling 162: 6986. Imberger J (1985) The diurnal mixed layer. Limnology and Ocean- ography 30: 737771. Imberger J and Patterson J (1990) Physical limnology. Advances in Applied Mechanics 27: 303475. Kundu PK and Cohen IM (2004) Fluid Mechanics, 3rd edn., 759 pp. San Diego: Academic Press. MacIntyre S (1993) Vertical mixing in a shallow eutrophic lake: Possible consequences for the light climate of phyoplankton. Limnology and Oceanography 38(4): 798817. Monismith SG (1986) An experimental study of the upwelling response of stratified reservoirs to shear stress. Journal of Fluid Mechanics 171: 407439. Monismith SG and Magnaudet JM (1998) On wavy mean flows, strain, turbulence and Langmuir cells. In: Imberger J (ed.) Physi- cal processes in Lakes and Oceans. Coastal and Estuarine Studies 54: pp. 101110. Washington DC: American Geophysical Union. Spigel RH and Imberger J (1980) The classification of mixed layer dynamics in lakes of small to medium size. Journal of Physical Oceanography 10: 11041121. Stefan H and Ford DE (1975) Temperature dynamics of dimictic lakes. Journal of Hydraulic Division, American Society of Civil Engineering 101(HY2): 334354. Thorpe SA (1977) Turbulence and Mixing in a Scottish Loch. Philosophical Transactions of Royal Society of London Series A 286: 125181. Wuest A and Lorke A (2003) Small-scale hydrodynamics in lakes. Annual Review of Fluid Mechanics 35: 373412. Hydrodynamics and Mixing _ The Surface Mixed Layer in Lakes and Reservoirs 221 Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes A Wu est, Eawag, Surface Waters Research and Management, Kastanienbaum, Switzerland A Lorke, University of Koblenz-Landau, Landau/Pfaly, Germany 2009 Elsevier Inc. All rights reserved. Introduction Density Stratification and Mixing the Basin Scale Nearly all lakes, reservoirs, and ponds that are deeper than a few meters, experience cycles of density stratifi- cation and destratification. Most important for this variation is the temperature-dependence of water density. During spring/summer or the wet season in the tropics the water is heated from above and a surface layer (SL: typically a few m thick) with warmer and hence lighter water develops on top of the cooler and heavier water below (Figure 1). In addition, although more important in saline lakes than fresh water ones, biological and hydrological processes may strengthen the density stratification by generating a vertical gradient in the concentration of dissolved substances (salinity). The resulting stratification is usu- ally depicted by a strong density gradient (also called pycnocline), separating the SL from the deeper reaches of the water column (indicated as metalimnion and hypolimnion in Figure 1). Mixing of heavier water from greater depth with lighter water from the SL implies that water parcels of different densities are exchanged in the vertical direction (Figure 2). It is evident that mechanical energy is needed to move these water parcels against the prevailing density gradi- ent, which forces lighter water up and heavier water down. The amount of energy needed to overcome ver- tical density stratifications is therefore determined by the potential energy DEpot (Figure 1) stored in the strati- fication. DEpot is calculated from the vertical separation of the centre of volume of the water body and its cen- ter of mass. Density stratification results in a lowering of the centre of mass by the vertical distance DhM (Figure 1) and the energy needed to overcome the strat- ification and to mix the entire water column is DEpot HrgDhM (Jm2 ), where H is the average depth of the water body, g is the gravitational accelera- tion, and r is the density. Density stratification thus imposes stability on the water column and reduces or even suppresses vertical mixing. Besides convective mixing in the SL caused by seasonal or nocturnal surface cooling in most lakes and reservoirs, the major source of energy for vertical mixing is the wind, whereas river inflows usually play a minor role (Figure 1). As water is 800 times denser than air and as momentum is conserved across the airwater interface, SLs receive only about 3.5% of the wind energy from the atmosphere above. Surface waves transport a portion of this energy to the shore where it is dissipated; the remaining energy causes large-scale currents, with surface water flows of 1.53% of the wind velocity. Moreover, surface currents cause a stratified water body to pivot with warm water piling up at the downwind end (causing downwelling) and deep-water accumulating at the upwind end (causing upwelling). After the wind ceases, the water displacement relaxes and various internal waves develop including basin-scale seiches inducing motion even in the deepest layers. These deep-water currents are usually one order of magnitude less energetic than those in the SL. Typical deep flows of a few centimeters per second (or $1 J m3 ) with energy dissipation of less than 1 mW m2 are able to reduce the potential energy of the stratification by only $0.010.05 mW m2 . Com- pared to the potential energy stored in the stratifica- tion (order of 1000 J m2 ; Figure 1) it would take much longer than one season to entirely mix a mod- erately deep lake. This implies that wind energy input (Figure 1) forms the vertical hypolimnion structure at times of weak stratification (beginning of the season), whereas the wind is not able to substantially change the vertical structure once the strong stratification is established. Therefore, in most regions on Earth, only very shallow waters (less than a few meters deep (such as Lake Balaton, Hungary) are found to be entirely nonstratified, even during the summer season. The majority of lakes and reservoirs deeper than a few meters are thus only partially mixed to a limited depth, which is basically defining the SL. For those lakes that show a pronounced SL, its maintenance is mostly supported by night-time cooling. In this arti- cle, we focus on the limited mixing below the SL, which occurs in the metalimnion and hypolimnion (Figure 1). Density Stratification and Mixing the Small Scale The same concepts of stability and mixing described in the preceding section for the entire water body also apply locally within the water column for small- scale vertical mixing of stratified layers. Local stability of the density stratification is quantified by the 222 Temperature density Temperature density Depth Depth Warm Warm Cold Cold W L Cold u u Warm Figure 2 The effect of turbulent mixing in a stable stratification: if the vertical gradient of horizontal currents (current shear @u=@z) is stronger then the stability of the water column (eqn. [1]), Kelvin Helmholtz instabilities can develop (top of middle panel) bringing warmer (lighter) and cooler (heavier) water in close proximity (bottom of middle panel). Finally, heat (or any other water constituent) is mixed by molecular diffusion across the manifold small-scale interfaces, which are generated by turbulence. The turbulent exchange of small water parcels leads to a fluctuating vertical heat flux (see example in Figure 3) which averages to a net downward heat flux. As a result, the original temperature profile (left) is modified (right): the gradient is weakened and expanded vertically with heat transported from top to bottom, and density vice versa, across the interface. Figure after the idea of Winters KB, Lombard PN, Riley JJ, and Dasaro EA (1995) Available potential-energy and mixing in density-stratified fluids. Journal of Fluid Mechanics 289: 115128. Experiments were first performed by Thorpe SA (1973) Experiments on instability and turbulence in a stratified shear-flow. Journal of Fluid Mechanics 61: 731751; and the phenomenon of sheared stratification in lakes was reported by Mortimer CH (1952) Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere. Philosophical Transactions of the Royal Society of London B: Biological Sciences 236(635): 355398; and by Thorpe SA (1977) Turbulence and Mixing in a Scottish loch. Philosophical Transactions of the Royal Society of London A: Mathematical Physics and Engineering Sciences 286(1334): 125181. Wind energy 104 to 102 Energy fluxes in W m2 Energy content in J m2 Center of volume Interior (stratified) Surface layer Metalimnion Hypolimnion Depth Density Temperature Stability Center of mass Ekin 1 to 100 hM Eheat 109 (summer winter) Epot 103 105 to 103 Inflow Net heat flux 200 to +200 Bottom boundary layer Figure 1 Energy fluxes (heat, wind, and river inflow; in red) into the water (W m2 ) and energy content (heat, kinetic energy, potential energy; in blue) stored in the lake water body (J m2 ). Note that the energy fluxes and contents related to heat are many orders of magnitude larger than those of kinetic and potential energy. The effect of mixing by the river is only local and less effective than wind. The stratified part of the lake (below surface layer) has historically been divided into the metalimnion (see large stability, right) and the deep hypolimnion (weak stratification) below. The lower water column can also be differentiated into an interior region (away from the boundaries) which is quiescent except during storms and a bottom boundary layer where turbulence is enhanced. Adopted from Imboden DM and Wu est A (1995) Mixing mechanisms in lakes. In: Lerman A, Imboden D, and Gat JR (eds.) Physics and Chemistry of Lakes, vol. 2, pp. 83138. Berlin: Springer-Verlag. Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes 223 Brunt-Vaisala frequency (also buoyancy frequency) N (s1 ), defined by: N2 g r @r @z 1 z is the depth (positive upward). As a result of wind- forced motions, a vertical gradient of the horizontal current u (shear @u=@z) is superimposed on the vertical density gradient @r=@z. Depending on the relative strength of N compared to the current shear @u=@z such a stratified shear flow may eventually become unstable and develop into turbulence (Figure 2). Although the large-scale (advective) motions are mainly horizontal, the turbulent eddies are associated with random velocity fluctuations in all three dimen- sions (u0 , v0 , w0 ). Turbulent kinetic energy (TKE) (Jkg1 ) is defined as the energy per unit mass of water which is contained in these velocity fluctuations: TKE 1 2 u02 v02 w02 2 In stratified turbulence, the vertical velocity fluctua- tions w0 are of particular importance as they transport water parcels and their contents in the vertical direc- tion (Figure 3). The product of the vertical velocity fluctuations w0 and the associated density fluctua- tions r0 describes an instantaneous vertical flux of density (w0 r0 (kg m2 s1 )). Resulting from many irregular and uncorrelated fluctuations (Figure 3) the averaged flux w0r0 leads to a net upward mass flux, which is usually expressed as a buoyancy flux Jb: Jb g r w0r0 3 Therefore, we can interpret vertical mixing as an upward flux of mass, which causes a change of the potential energy of the stratification (Figures 1 and 2), expressed as a buoyancy flux (eqn. [3]). The required energy originates from the TKE, which is itself extracted from the mean (horizontal) flow. Approxi- mately 90% of the TKE, however, does not contrib- ute to the buoyancy flux (and hence to vertical mixing) but is instead dissipated into heat by viscous friction, without any further effect. By defining local rates of production P (W kg1 ) and viscous dissipa- tion e(W kg1 ) of TKE, the simplest form of TKE balance can be formulated as: @ @t TKE P e Jb 4 1.5 1.0 0.5 0.0 0.5 1.0 1.5 Verticalvelocity (cms1 ) 0 5 10 15 20 25 30 216 0(a) (b) (c) 5 10 15 20 25 30 217 218 O2concentration (M) Time (s) 5 10 15 20 250 30 0.5 0.0 0.5 wO2 (Mcms1 ) Figure 3 Time series of O2 concentration (thin line, a) and vertical velocity w0 (thin line, b; positive upward), as measured 10 cm above the sediment in reservoir Wohlensee (Switzerland) at a frequency of 64 Hz. Red lines indicate the temporally varying averages, determined as running mean, whereas the black horizontal line marks the averages. Panel (c) shows the instantaneous eddy flux covariance of w0 and O2 0 : The average downward O2 flux over the 30 s ($1900 data pairs) is 6.4 mmol m2 day1 . Data source: Claudia Lorrai, Eawag. 224 Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes As mentioned above, the dissipation rate is usually much larger than the buoyancy flux, and hence the mixing efficiency gmix, which is defined as the ratio gmix Jb e gr1 w0r0 e 5 is much smaller than 1. A number of studies in stra- tified lakes and reservoirs have revealed typical mix- ing efficiencies in the range of 1015%. Density Stratification and Mixing the Turbulent Transport The local flux of a water constituent is given by the product of the velocity times the concentration. In stratified waters, the time-averaged vertical velocity is often close to zero (negligible) and thus, the vertical fluxes stem only from the fluctuations of velocity and concentration, such as explained above for the verti- cal mass flux w0r0 caused by the turbulence. This concept holds for any other water constituent, such as for oxygen, as exemplified in Figure 3, where the in situ measured w0 , O2 0 and the product w0 O2 0 is shown for a 30-s-long record. Although the momentary fluxes up and down are almost of equal variations and amounts, the averaging w0O 0 2 reveals slightly larger fluxes downwards to the sediment, where the oxygen is consumed. Until recently, direct measurements of turbulent fluxes had not been possible and therefore turbulent fluxes in stratified waters are commonly expressed using the eddy diffusivity concept. Applied to the mass flux w0r0 it implies assuming that (i) a well- defined local density gradient @r=@z exists (due to the stratification) and (ii) the flux in analogy to molecular diffusion can be expressed by the eddy (or turbulent) diffusivity Kz (m2 s1 ) multiplied by this local gradient: w0r0 Kz @r @z 6 In this formulation, Kz describes the vertical transport of density caused by turbulent velocity fluctuations w0 over a typical eddy distance L0 given by the level of turbulence and the strength of the stratification. Therefore, in contrast to the molecular diffusion pro- cess, eddy diffusivity is neither a function of medium (water) nor of the water constituents (particulate or dissolved), but rather a property of the turbulent flow within the stratified water itself. In particular, Kz reflects the extent of the velocity fluctuations w0 and the eddy sizes L0 : Kz can be interpreted as the statisti- cal average w0L0 of a large number of eddies, which exchange small water parcels as a result of the turbu- lent flow (Figures 2 and 3). In addition to density, all other water properties such as temperature or substances are transported and mixed in the same way via the turbulent exchange of small eddies or parcels of water (Figure 3). The eddy diffusivity concept can be applied to any dissolved or particulate substance and the associated vertical fluxes F can be readily estimated in analogy to eqn. [6] by F Kz@C=@z 7 where C is the appropriate concentration. Assuming steady-state conditions, i.e., by neglect- ing the left-hand side of eqn. [4], and combining eqns. [1], [5], and [6] yields: Kz gmix e N2 8 This equation provides an expression to estimate Kz from field measurements of e and N2 and, moreover, it demonstrates the direct proportionality of Kz on the level of turbulence (e) and the inverse proportionality on the strength of stratification (N2 ). In the last dec- ades, two fundamentally different approaches have been used for the estimation of Kz: (i) the microstruc- ture method and (ii) the tracer method. Method (i), is based on eqn. [8] where the dissipation of TKE or of temperature variations are measured by usually free- falling profilers which measure either temperature or velocity over small spatial scales. For example, spec- tral analysis of the temperature gradient signal pro- vides estimates of e and the local buoyancy frequency is obtained from density computed from the tempera- ture and salinity profiles. For the application of tracer method (ii), one has to measure the three-dimensional spreading of a tracer (artificial or natural) and then infer the diffusivities (Kz) from the observations. Heat is also used as a tracer and Kz is obtained by comput- ing a time series of the heat budget below the respec- tive depth of a lake. Typical values in stratified natural waters are listed in Table 1 and Figures 4 and 5. Turbulence is caused by current shear, breaking surface waves, and instabilities in the internal wave field. Currents induce shear near boundaries regard- less of whether the flow is stratified. Thus, the concept of eddy diffusivity is also applied to surface mixing layers and to nonstratified systems such as rivers. Turbulence and Mixing in Stratified Lakes and Reservoirs Turbulence Production in the Surface and Bottom Boundaries There are fundamentally two mechanisms generating turbulence in the SL: (i) the action of wind causing Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes 225 wave breaking and shear in the top few meters of the water column and (ii) surface cooling causing the sinking of heavier water parcels. Temperature-driven mixing (case (ii)) leads to homogenization of the SL and therefore to nonstratified conditions at least for a few hours or days before heat fluxes from/to the atmosphere restratify the SL. This process is discussed in detail elsewhere in this encyclopedia. Only in shal- low ponds or basins with relatively high through-flow will turbulence have other case-specific sources. For wind-driven mixing (case (i)), the crucial parameter governing the dynamics of turbulence in the SL is the surface shear stress t (N m2 ), the force per unit area exerted on the water by the wind. This stress is equal to the downward eddy-transport of horizontal momentum from the atmosphere. Part of t is consumed in the acceleration and maintenance of waves (tWave), whereas the remaining momentum flux tSL generates currents and turbulence in the SL. By assuming a constant stress across the airwater interface, the two momentum fluxes on the water side equal the total wind stress (t tSL tWave). Immediately below the waves, the momentum flux, tSL, drives the vertical profiles of horizontal velocity u(z) in the SL. If the wind remains relatively cons- tant for hours, quasi-steady-state conditions may develop in the SL: u(z) then depicts the Law-of- the-Wall @u=@z ukz1 tSL=r1=2 kz1 , where u tSL=r1=2 is the frictional velocity and k ( 0.41) is the von Karman constant. Because the buoyancy flux in the SL (defined in eqn. [3]) is not a large contribution in eqn. [4], we can assume a balance between the production of TKE and the rate of vis- cous dissipation (e) of TKE. This local balance between production and dissipation of turbulence determines the turbulence intensity as a function of depth throughout the SL. Under those assumptions, the dissipation e tSL=r @u=@z u 3 kz1 9 is only a function of the wind-induced stress tSL (here expressed as u*) and of depth z. Several experiments have demonstrated that dissipation is indeed inversely proportional to depth (eqn. [9]), if averaged for long enough. However, one has to be critical about the validity of eqn. [9] for two reasons: First, at the very top of the water column, breaking waves, in addition to shear stress, produce a significant part of the turbu- lence in the SL. This additional TKE generation at the surface can be interpreted as an injection of TKE from above. Therefore, in the uppermost layer, the turbu- lence exceeds the level described by eqn. [9], depend- ing on the intensity of the wave breaking. Second, Table 1 Typical values of dissipation, stability and vertical diffusivity in stratified waters Dissipationa (W kg1 ) Stability N2 (s2 ) Diffusivity* Kz (m2 s1 ) Ocean thermocline 1010 108 $104 (0.33) 105 Surface layer 106 109 0$105 105 102 Lake interior only (without BBL) 1012 1010 108 103 107 105 Metalimnion (basin scale) 1010 108 $103 (0.550) 107 Near-shore metalimnion 1010 106 $103 (0.33) 104 Deep hypolimnion (basin scale) 1012 1010 108 106 (0.033) 104 a During storm events values are larger by orders of magnitudes for short. 0 1 2 3 4 5 6 5 10 15 Time after tracer release (days) Verticalvariance2(m2) 20 25 30 0 Figure 4 Vertical spreading of the tracer Uranine after injection at 25 m depth in Lake Alpnach (Switzerland). The vertical line demarcates the initial period of 7 days, during which Uranine resided in the interior of the stratified deep water. The two insets show the lake area at the surface and at the depth of the Uranine injection, as well as the horizontal distribution of the Uranine cloud (shaded in gray) after 4 and 28 days. The slow growth of the spreading in the first 7 days illustrates the quietness in the interior. The fast growth of the vertical spreading after day 7 is due to the increasing contribution of BBL mixing after the tracer has reached the sediment at 25 m depth. Reproduced from Goudsmit GH, Peeters F, Gloor M, and Wu est A (1997) Boundary versus internal diapycnal mixing in stratified natural waters. Journal of Geophysical Research 102: 2790327914, with permission from American Geophysical Union. 226 Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes eqn. [9] relies on quasi-steady-state conditions which may hold applicable for limited episodes only. Despite these restrictions, eqn. [9] gives a good estimate of the diffusivity in the SL, if it is weakly stratified. Equations [8] and [9] reveal that the rate of mixing increases substantially within the SL as the surface is approached. The corresponding stability N2 decreases at the surface and maintains rapid mixing. Therefore, gradients of temperature, nutrients, and par- ticulates are usually smallest at the surface and increase with depth. During sunny days, diurnal thermoclines form with mixing reduced below them. On cloudy, windy days, the SL may mix fully and may even deepen depending upon the surface forcing. Factors that affect the depth of mixing are discussed elsewhere in this encyclopedia. It is typically a few m during the warm season and a few tens of meters during the cold season. Below, a strong density gradient (pycnocline) can develop leading to the separation between the SL and the metalimnion/hypolimnion. In the stratified interior (away from the BBL; see below), the effect of wind is shielded and the mixing regime is completely different. As discussed in greater detail (see The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs)), turbulence generation and mixing along the bottom boundaries of water bodies can be described in anal- ogy to the SL. Under steady-state conditions, the resulting bottom boundary layer (BBL) follows a similar vertical structure of (i) current shear (see above), (ii) rate of TKE dissipation (eqn. [9]) and (iii) rate of vertical mixing. Although the original indirect driving force for turbulence in the BBL is also the wind, it is not the direct turbulent momentum flux from the atmosphere to the water which is the cause. Rather, the mechanism is indirectly induced by wind which causes large-scale currents and basin-wide inter- nal waves (such as seiches) which act as intermediate energy reservoirs that generate TKE by bottom fric- tion. Along sloping boundaries in particular, the break- ing of propagating internal waves and convective processes a secondary effect of bottom friction can produce additional TKE, leading to dissipation and mixing in excess of that predicted by eqn. [9]. As with the SL, the BBL is also usually partly (and weakly) stratified. Again, mixing (eqn. [8]) increases substan- tially when approaching the sediment and often a completely homogenized layer a few m thick develops at the bottom. Internal Waves and Turbulence in the Stratified Interior In the lake interior, away from surface and bottom boundaries (Figure 1), the water body is stratified and quiescent, and it does not feel the direct effects of the turbulence sources at the surface and above the 50 100 150 200 Depth(m) 250 300 350 0 1 3 4 2 5 6 Ice cover Vetrical diffusivity (m2 s1) 1 3101 1 3102 1 3103 1 3104 1 3105 400 50 100 150 Day of the year 200 250 3000 350 Figure 5 Vertical diffusivities in Lake Baikal simulated with a k-epsilon model. The numbers (16) on the contour plot indicate the main features of the seasonal stratification and changes in diffusivity: the formation of thermal stratification with weak mixing (1) during winter under the ice and (2) during summer; (3) the formation of a convectively mixed layer in spring under the ice; the deep convective mixing in (4) June and (5) November; and (6) the formation of a mixed layer near the temperature of maximum density. Here the emphasis is on the temporal and vertical structure of the turbulent diffusivity and not on the absolute accuracy, which may be difficult to achieve with turbulence modeling better than a factor of 23. Reproduced from Schmid M et al. (2007) Sources and sinks of methane in Lake Baikal: A synthesis of measurements and modeling. Limnology and Oceanography 52: 18241837, with permission from American Society of Liminology and Oceanography. Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes 227 sediment. This stratified interior consists of an upper region, the metalimnion where gradients in tempera- ture and density are strongest, and a lower region, the hypolimnion, which is only weakly stratified and most water properties are homogeneous. Internal waves are prevalent. The rate of mixing in the interior water body is low because (i) currents and shear are weak and the resulting turbulence production is reduced and (ii) stratification suppresses the turbulent mixing. The mechanical energy originates mainly from basin- scale internal currents and waves (see above), whereas the waves of smaller scale and higher frequencies potentially generated at a few specific locations are not contributing much to the energy budget of the deep-water. At the transition between small- and large-scale waves are the near-inertial currents, which can carry especially in large lakes a signi- ficant portion of the mechanical energy typically in the order of $1 J m3 . Given that observed energy residence time-scales are days (small lakes) to weeks (deepest lakes), the dissipation of the internal energy is $1012 $1010 W kg1 (Table 1). Considering typical values for stratification N2 (eqn. [1]) of 108 103 s2 and gmix % 0:1 (eqn. [5]), interior diffu- sivities of 107 105 m2 s1 can be expected (Table 1; Figure 4). The stratified interior away from the SL and the BBL is by far the most quite zone in lakes. Important for the generation of small-scale mixing are local instabilities related to internal (baroclinic) motions, such as illustrated in Figure 2. Instabilities occur mostly where the usually weak background shear is enhanced by nonlinear steepening of internal waves or by superposition of the shear with small- scale propagating internal waves. Direct observations of turbulence and mixing, using microstructure and tracer techniques, confirm that turbulence is indeed very weak in the stratified interior. Typically, only a few percent of the water column is found to be actively mixing. The occur- rence of such turbulent patches is highly intermittent in space and time. During periods when the fluid is nonturbulent, we can expect laminar conditions and thus the dominance of molecular transport. The observable average diffusivity can be considered the superposition of a few turbulent events separated by molecular diffusion for most of the time. The resulting transport in the stratified interior will therefore be close to molecular. Tracer experiments and microstructure profiling conducted in small and medium-sized lakes confirm these quiet conditions in the interior and enhanced turbulence in the bottom boundary. In Figure 4 the vertical spreading of a tracer, injected into the hypolimnion, is shown for the interior (first few days) and for a basin-wide volume including the BBL (after a few days). From Figure 4 it is evident that turbulent diffusivity in the interior is at least one order of magnitude lower than in the basin-wide deep-water volume, including the bottom boundary. In addition to these spatial differ- ences, one has to be aware of the temporal variability. During storms, turbulence can be several orders of magnitude larger for short episodes. The transition from quiescent to actively mixing occurs rapidly once winds increase above a certain threshold relative to the stratification. The internal wave field is energized and turbulence can develop. But the greatest increases occur in the benthic BBL. It is during such storms that most of the vertical flux takes place. The turbulent patches, where vertical fluxes are generated (as exemplified in Figure 3) vary in size depending in part upon the turbulence intensity e and the stratification N2 . Several length scales have been developed to characterize the sizes of turbulent eddies. One is the Ozmidov scale LO e=N3 1=2 10 and the other is the Thorpe scale, LT, which is based on direct observations of the size of unstable regions. The ratio of the two numbers varies depending upon the strength of stratification and is useful for predict- ing the efficiency of mixing, gmix in eqn. [5] Typical values for LO and LT range from a few centimeters to a meter but for weak stratification eddies are larger and on scales of tens of meters to 100 m as found in weakly stratified Lake Baikal. The spatial and temporal dynamics of mixing chal- lenges not only the experimental estimation, but also the numerical simulation of its net effect, in terms of a turbulent diffusivity Kz. Local measurements of Kz following eqn. [8] often neither resolve its spatial nor its temporal dynamics and the coarse grid sizes used in numerical simulations do not capture the small scales relevant for mixing processes in the interior. Turbulent Energy Flux through the Water Column Synthesis From the discussion above, we can draw the follow- ing overall scheme of the energy flux through the stratified waters of a lake. The origin of the energy for turbulent mixing is usually wind, which is imposing momentum onto the surface of the water. Approximately 3% of the wind energy from the atmosphere reaches the epilimnion in the form of horizontal currents and about 10% thereof is finally transferred to the stratified water body underneath. The major part of the energy is dissipated by bottom interaction, and the minor part is dissipated in the 228 Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes interior by shear instabilities and breaking of internal waves. Of this dissipated energy, only about 10% produce buoyancy flux (mixing efficiency gmix, eqn. [5]) increasing the potential energy of the stratifica- tion. Compared to the wind energy flux in the atmo- sphere, only a small fraction of $0.0003 actually causes the mixing against the stratification in the deep water, whereas the large fraction of $0.9997 is dissipated somewhere along the flux path. Although this partitioning depends on many factors, the overall scheme likely holds within a factor of 23 based on comparisons between different lakes. The small amount of energy available for mixing compared to the potential energy stored in the stratification explains why lakes deeper than a few meters remain permanently stratified during the warm season. Consistent with this conclusion, the enhanced turbulence in the surface and bottom boundary layers cannot erode the stable and partly very strong stratification in the interior. Turbulent patches are intermittent and the eddies within them are small com- pared to the depth. As an example, the timescales to transport heat, solutes or particulates over a distance of 10 m would be (10 m)2 Kz 1 ; i.e., several years for a Kz 106 m2 s1 in the metalimnion (Table 1). There- fore, two-dimensional processes, such as upwelling become important for vertical exchanges as well. See also: The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs); Currents in Rivers; Currents in Stratified Water Bodies 1: Density-Driven Flows; Currents in Stratified Water Bodies 2: Internal Waves; Currents in Stratified Water Bodies 3: Effects of Rotation; Currents in the Upper Mixed Layer and in Unstratified Water Bodies; Density Stratification and Stability; Hydrodynamical Modeling; The Surface Mixed Layer in Lakes and Reservoirs. Further Reading Goudsmit GH, Peeters F, Gloor M, and Wuest A (1997) Boundary versus internal diapycnal mixing in stratified natural waters. Journal of Geophysical Research 102(C13): 2790327914. Mortimer CH (2005) Lake Michigan in Motion: Responses of an Inland Sea to Weather, Earth-Spin, and Human Activities. University of Wisconsin Press. ISBN 978-0299178345. Imberger J (1998) Physical Processes in Lakes and Oceans. Coastal Estuarine Studies, vol. 54. Washington, DC: American Geophys- ical Union. Imberger J and Ivey GN (1991) On the nature of turbulence in a stratified fluid. Part II: Application to lakes. Journal of Physical Oceanography 21: 659680. Imberger J and Patterson JC (1990) Physical limnology. Advances in Applied Mechanics 27: 303475. Ivey GN, Winters KB, and Koseff JR (2008) Density stratification, turbulence, but how much mixing? Annual Review of Fluid Mechanics 40: 169184. Kantha LH and Clayson CA (2000) Small Scale Processes in Geo- physical Fluid Flows. International Geophysical Series, vol. 67. London: Academic Press. ISBN-10: 0-12-434070-9. Imboden DM and Wuest A (1995) Mixing mechanisms in lakes. In: Lerman A, Imboden D, and Gat JR (eds.) Physics and Chemistry of Lakes, pp. 83138. Berlin: Springer-Verlag. MacIntyre S, Flynn KM, Jellison R, and Romero JR (1999) Bound- ary mixing and nutrient flux in Mono Lake, CA. Limnology and Oceanography 44: 512529. Schmid M, et al. (2007) Sources and sinks of methane in Lake Baikal: A synthesis of measurements and modeling. Limnology and Oceanography 52: 18241837. Thorpe SA (2007) An Introduction to Ocean Turbulence. Cambridge, UK: Cambridge University Press. ISBN: 978-0-521- 85948-6. Winters KB, Lombard PN, Riley JJ, and Dasaro EA (1995) Available potential-energy and mixing in density-stratified fluids. Journal of Fluid Mechanics 289: 115128. Wuest A and Lorke A (2003) Small-scale hydrodynamics in lakes. Annual Review of Fluid Mechanics 35: 373412. Wuest A and Lorke A (2005) Validation of microstructure-based diffusivity estimates using tracers in lakes and oceans. In: Baumert HA, Simpson J, and Sundermann J (eds.) Marine Turbulence Theories, Observations and Models. Cambridge, UK: Cambridge University Press. ISBN: 0521837898. Hydrodynamics and Mixing _ Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes 229 The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) A Lorke, University of Koblenz-Landau, Landau/Pfaly, Germany S MacIntyre, University of California, Santa Barbara, CA, USA 2009 Elsevier Inc. All rights reserved. Introduction Definition and Relevance of the Benthic Boundary Layer The benthic boundary layer (BBL) of lakes, reservoirs, and rivers constitutes that part of the water column that is directly influenced by the presence of the sediment water interface. Similar to the surface mixed layer, it represents a hot spot not only of dissipation of kinetic energy, but also of biological activity and of geochemical transformation processes. These different processes are strongly coupled and interact with each other: While the hydrodynamic conditions are modified by biological activity, which changes the structure of the sediment surface, the release of dissolved solids from the sediment can modify the density stratification in the BBL. More- over, the actual sediment surface cannot always be regarded as rigid since the BBL flow does not only modify the structure of the sediment surface, but it can also bring sediment particles into suspension, whereas at other sites or at other times, the particles resettle. The BBL definition provided here and the more detailed discussions later explicitly refer to direct influences of the sediment surface. From a more gen- eral point of view, the BBL is of great importance for the entire water body, almost independent of the dimensions of the basin. Strong turbulence and mix- ing along the boundaries are known to be important for vertical mixing, and transport on a basin scale and biogeochemical processes at the sediment surface or within the sediment effect the distribution of relevant water constituents on scales much larger than the actual dimensions of the BBL. These larger-scale effects, however, require additional transport pro- cesses for energy and matter into or out of the BBL and are considered elsewhere. A major characteristic of the BBL is the magnitude and the temporal dynamics of the physical forcing, i.e., the current velocity at the top of the BBL. Although in most rivers this forcing can be regarded as a steady-state unidirectional flow, its nature in deep and stratified lakes and reservoirs is more com- plex. In these, usually stratified, water bodies the major energy is provided by surface waves in the shallow littoral zone, by high-frequency internal waves at the depth of the thermocline and by basin- scale internal waves (seiches or Kelvin and Poincare waves) in the hypolimnion. Hence, the magnitude and temporal dynamics of the different forcing mechanisms range from current velocities of some 10 cm s1 and time scales of seconds for surface waves, to typical current velocities of a few centimeters per second and time scales of several hours to days for basin-scale internal waves (Figure 1). Structure of the BBL The BBL can be structured vertically according to the physical processes governing the vertical transport of momentum and solutes (Figure 2). In an outer layer (turbulent BBL) up to several meters above the sedi- ment surface, this transport is governed by turbulent eddies and the associated mixing rates are high. While approaching the sediment surface down to scales where viscous forces suppress overturning turbulent motions, the vertical transport of momentum is gov- erned by molecular viscosity and a viscous sublayer withatypicalheight of O(1cm) develops. The exchange of heat and dissolved solids and gases is eventually controlled by a diffusive sublayer with a height of O (1 mm) directly at the sedimentwater interface. The Transport of Momentum The Turbulent BBL The equation for total average shear stress t in a turbulent boundary layer is t m du dz u0w0 1 where m is dynamic viscosity, du/dz is the vertical velocity gradient, u0 and w0 are the fluctuating hori- zontal and vertical velocities, and the overbar denotes temporal averaging. While the first term on the right describes viscous shear, the second term is related to momentum transport by turbulent velocity fluctua- tions. In most aquatic systems, the Reynolds number associated with near-bottom flows is sufficiently high to sustain a turbulent boundary layer. Under such conditions, the first term on the right-hand side of eqn [1] may be negligible and turbulent shear stress is likely to dominate the shear stress computation. On the basis of dimensional arguments, it can be assumed that the shear stress, t, on the sediment 230 surface is related to the current speed at a certain height above the sediment: t CDU2 1m 2 where r is the density, CD an empirical constant (%1.5 103 ), the so-called drag coefficient, and U1 m refers to the current speed measured at a height of 1 m above the sediment surface. Note that CD depends on the reference height where the current speed was measured and a standard height of 1 m is assumed from now on. The bed shear stress t is assumed to be constant throughout the boundary layer (constant stress layer) and it is used to define a turbulent velocity scale u*, the so-called friction velocity: u t r 3 Dimensional analysis can then be used to deduce the velocity distribution u(z) near the sediment surface, 103 102 101 100 Heightabovesediment(m) Turbulent boundary layer (logarithmic layer) Viscous sublayer Diffusive sublayer Sediment Figure 2 Idealized structure of the BBL on a flat sediment surface. Note that the heights provided by the logarithmically scaled axis represent order of magnitude estimates for typical conditions found in inland water bodies. Time (24 Aug 2005) 4 days13min Currentspeed(ms1) Currentspeed(ms1) 10m depth 100m depth (c) (d) 0.1 0.10 0.05 0.00 0.05 0.10 0.1 0.0 19:30 20:00 20:30 21:00 Date (2001) 15 Oct 22 Oct 29 Oct 5 Nov 3 s Surface Thermocline Currentspeed(ms1) Depth(m) 1m depth (a) (b) 0.2 0.1 0.0 0.1 0.2 100 10 0 Time (16 Nov 2006) 16:22:10 16:22:18 16:22:26 16:22:34 1 2 3 1 32 Figure 1 Typical near-bottom current velocities measured at various locations (depths) in a large Lake (Lake Constance) emphasizing the different periods and magnitudes of BBL forcing. (a) A schematic cross-section of the lake with the three sampling sites indicated by numbers. Near-bottom current velocities induced by surface waves at 1-m depth are shown in panel (b). Typical periods of surface waves in lakes are in the order of seconds. (c) Near-bottom current velocities measured at the depth of the seasonal thermocline (10-m depth). The observed current velocities are driven by propagating internal waves with periods between 8 and 20 min. Near-bottom currents at 100-m depth (d) are mainly driven by basin-scale internal waves. The major period of about four days is associated with a Kelvin wave. Note that several other basin-scale modes of oscillation (e.g., 12 h) are superimposed on this four-day period. Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) 231 where z is the distance from the sediment surface. For a layer far enough from the boundary so that the direct effect of molecular viscosity on the flow can be neglected (the outer layer), the analysis results in uz u k ln z z0 4 where k % 0.41 is von Karmans constant and z0 is the roughness length, which is related to the drag coeffi- cient in eqn [2] by C1m k ln 1m ln z0 2 5 and will be discussed later. Equation [4] is called law of the wall, and by assuming a local steady-state equilibrium between production and dissipation of turbulent kinetic energy (TKE), it can be used to estimate the vertical distribution of the turbulence dissipation rate e e u3 kz 6 Thus, in analogy to the wind-forced surface layer, the level of turbulence increases with decreasing dis- tance from the boundary. This increasing turbulence leads, again in analogy to the surface mixed layer, to the development of a well-mixed boundary layer of up to several meters in height. The Viscous Sublayer It should be noted that eqn [4] is strictly valid for turbulent flows only for which the vertical transport is governed by cascading turbulent eddies. The maxi- mum (vertical) size of the turbulent eddies is deter- mined by the distance from the sediment surface, and by approaching the sediment surface down to scales where overturning turbulent motions are suppressed by the effect of molecular viscosity, the momentum transport becomes governed by viscous forces (first term on the right-hand side of eqn [1]). Within this layer, which is called the viscous sublayer, current shear becomes constant and the resulting linear veloc- ity profile can be described by uz u2 n z 7 On a smooth sediment surface, the viscous sublayer extends to a height dn of about 10n/u*, which is comparable to the Kolmogorov microscale describing the size of the smallest turbulent eddies (typically O (1 cm), cf. Figure 2). Since viscosity is reduced to its molecular value, current shear within the viscous sublayer is greater than that in the turbulent layer above (cf. Figure 3), a fact which has major consequences for organisms living within the viscous sublayer on the sediment sur- face because they have to withstand these strong shear- ing and overturning forces. It is further interesting to note that an appreciable amount of energy entering the BBL is dissipated within this layer (about 40%). Effects of Bottom Roughness The roughness length z0 in eqn [3] determines the effective height above the bottom z at which the current velocity approaches zero. It is determined by the topographic structure of the sediment surface and hence by the typical height, width, and spacing of individual roughness elements on a stationary bed. When the scale of these roughness elements zS is on the order of the height of the viscous sublayer dn or less, z0 is solely determined by dn and z0 % 0.1n/u*. This flow regime is called smooth. When the size of the roughness elements exceeds dn, the flow regime is called rough and the corresponding roughness length is given by z0 % zS/30. Note that the drag coefficient CD % 1.5 103 provided earlier (eqn [2]) corre- sponds to a roughness length z0 % 2.5 105 m (eqn [5]) and hence is valid for smooth flows unless u* exceeds 0.4 m s1 or U1 m exceeds 10 m s1 . In addition to the shear stress derived from viscous forces as described above (the so-called skin friction), larger-scale roughness elements can cause a form drag, which results from pressure gradients between the upstream and downstream side of particular roughness elements. Although skin friction is impor- tant for the lower part of the turbulent BBL and for z 0 Linear Logarithmic Viscous sublayer u Figure 3 Velocity distribution above a smooth and rigid bottom (solid line). Within the viscous sublayer the velocity u increases linearly with distance from the sediment surface z. Above the viscous sublayer the velocity distribution follows the law of the wall (eqn [4]) and increases logarithmically with distance from the surface. Extrapolated continuations of the linear and logarithmic velocity distributions are shown as dashed lines. 232 Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) the viscous sublayer, form drag resulting from, e.g., ripples, sand waves, or submerged vegetation is more important for the upper part of the turbulent BBL and for the total drag on flow. When form drag is signifi- cant, the turbulent BBL may consist of more than one logarithmic layer, described by different roughness lengths z0, respectively. Oscillatory Boundary Layers The turbulent BBL equations derived here are based on steady-state conditions, i.e., on a local balance between production and dissipation of TKE, which is in equilibrium with the applied forcing. As described later, however, many forcing mechanisms for near-bottom flows are related to surface or inter- nal waves and are hence associated with oscillatory flows. Well above the viscous sublayer, such oscilla- tory BBL show, similar to the effect of form drag, deviations of the of the velocity distribution from its steady-state logarithmic pattern. One major charac- teristic of oscillatory BBL is a pronounced maximum of the current speed at some decimeters or meters above the bed. The analytical solution to this problem (Rayleigh flow or Stokessecond problem) is an expo- nentially damped vertical oscillation of the current profile with a vertical wave number of o=2n p , where o is the forcing frequency and n the turbulent viscosity, which, however, is a function of time and distance from the sediment surface. Depending on the overall energetics of the BBL flow, characteristic cur- rent speed maxima at 23 m above the bed could be observed in lakes where the internal wave forcing had a period as long as 24 h. Another major consequence of oscillatory BBL is that the maximum in turbulent intensity near the bed does not coincide with the maximum of the current speed, at the top of the BBL. Stratified BBL Effects of Density Stratification Density stratification affects turbulent mixing in the outer layer by causing buoyancy forces that damp or even suppress overturning turbulent eddies. The verti- cal distribution of velocity and turbulence described earlier for unstratified BBL may hence change signifi- cantly under stratified conditions. In addition, the ver- tical structure of density stratification along with the presence of sloping boundaries can introduce addi- tional mixing phenomena in BBL of enclosed basins. Similar to the surface mixed layer, increased pro- duction of TKE along the boundaries of a water body often leads to the generation and maintenance of a well-mixed BBL of height hmix. On a flat bottom (away from the slopes) and where a logarithmic bound- ary layer occurs, hmix can be estimated by applying scaling laws from the wind-mixed surface layer hmix 23=4 u Nf p 8 where u* is the friction velocity in the BBL (eqn [2]), N is the BruntVaisala frequency, and f is the Coriolis parameter. In small- to medium-sized water bodies, where the effect of Earths rotation is unimportant, f has to be replaced by the respective forcing frequency, e.g., the frequency of internal seiching. In productive water bodies, in particular, the sedi- ment can be a significant source of remineralized nutri- ents as a result of microbial degradation of organic matter at the sediment surface or within the sediment. The diffusion of solutes across the sedimentwater interface (see Solute Transport and SedimentWater Exchange section) has the potential to set up density stratification within the BBL, which could suppress turbulent mixing. Hence, whether or not a turbu- lent and mixed BBL can be developed and main- tained depends not only on the amount of available TKE, which is typically extracted from basin-scale motions, but also on the buoyancy flux from the sediment that has to be overcome by turbulent mix- ing. Geothermal heating, in contrast, can result in unstable stratification and convective mixing in the BBL. A mean geothermal heat flux of 46 mW m2 results in a mean vertical temperature gradient of about 8 102 K m1 , which can be observed when the BBL is chemically stratified and turbulent mixing is suppressed. 2-Dimensional Mixing Processes in Enclosed Basins The occurrence of mixed BBL (in terms of density) is a straight consequence of the application of a zero-flux boundary condition at the sediment surface, i.e., no exchange of heat and dissolved solids across the sedimentwater interface. This boundary condition forces the isopycnals (or isotherms if density changes are mainly caused by temperature) to intersect the boundary at a right angle, leading to a mixed density or temperature profile in the vicinity of the bound- ary. Enhanced mixing along the boundaries is thus not a necessary requirement for the development of such mixed layers. Along the sloping boundaries of enclosed basins, these mixed BBL cause horizontal den- sity gradients and hence drive horizontal currents a process which is believed to have important con- sequences for basin-wide diapycnal transport. Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) 233 Measurements, however, have revealed that hmix is not constant along the sloping boundaries, as demon- strated in Figure 4. There the upper limit of the mixed BBL can be defined by the depth of the 5 C isotherm (chemical stratification can be neglected in this par- ticular lake), leading to hmix 2.3 m in the central part of the lake, whereas hmix 1 m further up on the slopes (Figure 4(b)). The pronounced tilt of the iso- therms in Figure 4(a) further emphasizes the impor- tance of basin-scale internal waves for local estimates of hmix on the slopes because the associated currents push the well-mixed BBL from the central part of the lake up and down the respective slopes during the course of the seiching. The flow within the BBL remains parallel to the sediment surface on the sloping boundaries because the vertical velocity component must vanish at a rigid surface. Hence the flow is no longer in parallel to the isopycnals (or isotherms in Figure 4(a)) and, in com- bination with the fact that the flow velocity is increas- ing with increasing distance from the sediment surface (eqn [4]), convective instabilities can occur on the slopes when heavier water is moved on top of lighter water. Unstable stratification, as shown in the inset of Figure 4(b), can only be generated when the current is directed up-slope, a down-slope current leads to a stabilization of the BBL by the same principle. Thus, in a periodic, internal wave-driven flow, stratified and convectively mixing BBL occur alternately on the two opposing slopes of the water body. This shear-induced convection provides an additional source for mixing in BBL on slopes. Its general importance for BBL turbulence, however, is not yet fully understood. Turbulence Induced by Internal Wave Interactions with Bottom Boundaries Turbulence production in stratified regions of lakes is linked with instabilities in the internal wave field. A considerable portion of the turbulence occurs within or near the BBL and can be due to internal wave break- ing at critical frequencies or internal wave steepening. Recent studies have shown that the form and degree of nonlinearity of internal waves in the thermocline can be predicted from the Wedderburn and Lake numbers, two dimensionless indices which indicate the balance between buoyancy forces and shear forces and which further take into account basin morphometry. As illu- strated in Figure 5, the hypolimnion is also an internal wave field with similar wave forms to those observed in the thermocline. When Lake numbers, LN, drop below 3, turbulence associated with the internal wave field increases (Figure 5). Thus, not only is turbulence induced in the thermocline when nonlinear waves form, but also in the hypolimnion with the greatest increases in the BBL. Values of the coefficient of eddy diffusivity increase 13 orders of magnitude above mo- lecular. In small lakes, flow speeds in the BBL increase from a few millimeters per second to $2 cms1 with the decreases in Lake number. Solute Transport and SedimentWater Exchange The Diffusive Sublayer In the immediate vicinity of the sediment surface, the vertical transports of momentum and solutes 10 2 5 0 5 6 7 0 4.98 5.00 1 2 3 Temperature (C) Heightabovesediment(m) 1 3 30 25 20 15 6.5 7.0 6.0 5.0 Depth(m) Distance (m)(a) (b) 1000 2000 3000 5.51 2 3 Figure 4 (a) Isotherm depths along the main axis of Lake Alpnach (Switzerland) calculated from repeated CTD profiling. The increment between neighboring isotherms is 0.1 C and the numbers refer to the respective temperature (in C) of the isotherms plotted as thick lines. Note that the figure is not to scale and only the lower portion of the water column is shown. The numbered symbols show the position of temperature profiles shown in (b). (b) Near-bottom temperature profiles at selected positions along the transect shown in (a). Numbers at the top of the profiles refer to the positions indicated by symbols in (a). The inset emphasizes the inverse temperature stratification observed in the BBL of profile 2. Panel (a) is adopted from Lorke A, Wu est A, and Peeters F (2005) Shear-induced convective mixing in bottom boundary layers on slopes. Limnology and Oceanography 50: 16121619, with permission from American Society of Limnology and Oceanography. 234 Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) (dissolved gases, solids, and heat) are reduced to their respective molecular levels, as described above. In analogy to the viscous sublayer, where momentum transport is governed by molecular viscosity, a diffu- sive sublayer exists, where the vertical transport of heat and solutes is governed by molecular diffusion. Since the molecular diffusivity of solutes D is about 3 orders of magnitude smaller than the molecular vis- cosity n (the Schmidt number Sc, defined as Sc n/D, is about 1000), the height of the diffusive sublayer dD is with dD O(1 mm) considerably smaller than the height of the viscous sublayer dn (Figure 2). A typical profile of dissolved oxygen concentrations measured through the sedimentwater interface is shown in Figure 6. Although turbulent transport is already suppressed within the viscous sublayer, straining of concentration gradients by viscous shear results in an efficient vertical transport of solutes and to typically well-mixed solute distributions within most of the viscous sublayer. Concentration gradients are hence compressed to the diffusive sublayer overlaying the sediment surface and the constancy of the molecular diffusivity results in a linear concentration gradient C (z) (Figure 6). At the top of the diffusive boundary layer, the concentration gradient decreases gradually to zero and the solute concentration reaches its con- stant bulk value C1. Within the sediment, molecular diffusivity is re- duced by the porosity (reduction of surface area) and by turtosity (increase of diffusion path length), and the concentration profile is additionally deter- mined by chemical and microbial production and 195.3 195.4 195.5 195.6 195.7 195.8 195.9 6 8 10 12 14 16 18 20 Day of year Depth(m) Figure 5 Isotherms illustrating the internal wave field in the hypolimnion of Toolik Lake, Alaska, prior to and after wind forcing increased to 9 m s1 (day 195.6) and the Lake number decreased to 1.5. Isotherms are at 0.1 C intervals with uppermost isotherm 6 C. Thermistors were 80 cm apart between 10.2 and 12.6 m depth and 2 m apart deeper in the water column. Deepest thermistor was within 50 cm of the lake bottom. Increased temperature fluctuations after LN decreases below 1.5 are indicative of turbulence either beginning or increasing in the lower water column (unpublished data, S. MacIntyre). 1 0 1 2 Oxygen concentration (mg L1) Heightabovesediment(mm) Water 0 2 4 6 8 10 Sediment dD O2 Figure 6 Oxygen concentration profile across the sedimentwater interface measured in Lake Alpnach (Switzerland). The diffusive sublayer is characterized by the linear concentration gradient above the sediment surface where transport is governed by molecular diffusion. The effective height of the diffusive sublayer dD is defined by the intersection of the extrapolated linear concentration gradient (dashed line) with the constant oxygen concentration above the diffusive sublayer. Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) 235 loss processes. In the case of oxygen (Figure 6), a reactiondiffusion model with rather simple zero- order kinetics of oxygen consumption resulting in a parabolic oxygen profile provides surprisingly good agreement with measured oxygen distributions. The fluxes F of solutes through the diffusive bound- ary layer can be derived from Ficks first law: F D dD C1 C0 9 where C0 is the solute concentration at the sediment surface. Hence, for a given concentration gradient (C1 C0) and by ignoring the temperature depen- dence of the molecular diffusivity, the magnitude of the flux is determined by the thickness of the diffusive sublayer dD. It has been demonstrated in numerous laboratory and field measurements that dD depends strongly on the flow regime in the turbulent BBL above. With increasing levels of turbulence (e.g., with increasing u*) the diffusive boundary layer becomes more compressed, and according to eqn [9], the fluxes increase. The thickness of the diffusive sublayer can be related empirically to u* or to the thickness if the viscous sublayer, which in turn is related to u*, as described earlier: dD dSca 10 where the Schmidt number Sc accounts for the differ- ent kind of solutes (e.g., heat or dissolved oxygen) and observed Schmidt number exponents a range between 0.33 and 0.5. As u* is not always an appro- priate parameter for describing BBL turbulence (e.g., in oscillatory BBL or in the presence of form drag or density stratification), dD can also be described in terms of the Batchelor length scale, which describes the size of the smallest fluctuations of a scalar tracer in turbulent flows as a function of the turbulence dissipation rate. It is most interesting to note that the sedimentwater exchange in productive water bodies is often flux- limited by the bottleneck of the diffusive sublayer and that it is actually the wind acting at the water sur- face that provides energy for turbulence within the BBL and hence effects the magnitude of the sedimentwater fluxes by controlling the thickness of the diffusive sublayer. Effects of Small-Scale Sediment Topography Increased roughness of the sediment surface (e.g., due to biological activity) affects the sedimentwater exchange by increasing the mass and momentum transfer as well as by increasing the surface area of the sedimentwater interface. Detailed observations have demonstrated that the diffusive sublayer tends to smooth out topographic structures that are smaller than the average height of the sublayer, but smoothly follows larger roughness elements (Figure 7). The detailed structure of the oxygen distribution within the diffusive sublayer is then not only determined by diffusion (normal to the local sediment surface) but also by advection with the flow (in parallel to the local sediment surface) and it can be expected that the degree of smoothing increases with decreasing flow velocities. Detailed comparisons of measured 3-dimensional fluxes over rough topography with 0 1 2 3 4 mm mm Microbial mat Water Flow 0 4 8 12 16 20 24 1 2 3 4 Figure 7 Horizontal transect along the direction of flow showing how the upper limit of the diffusive sublayer (solid line with data points) follows the surface topography of a microbial mat. The diffusive sublayer limit was defined by the isopleth of 90% air saturation of oxygen. Notice different vertical and horizontal scales. Flow velocity at a height of 1 cm was 4 cm s1 . Numbers indicate specific measuring positions discussed in the original publication. Reproduced from Jrgensen BB and Des Marais DJ (1990) The diffusive boundary layer of sediments: Oxygen microgradients over a microbial mat. Limnology and Oceanography 35:13431355, with permission from American Society of Limnology and Oceanography. 236 Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) the fluxes calculated from the respective average dif- fusive sublayer heights and concentration gradients are enhanced by factors up to 49%. It must be noted, however, that fluxes estimated from concentration profiles measured at one particular location on a rough sediment surface can severely overestimate or underestimate the average flux, as demonstrated in Figure 7. Nondiffusive Fluxes Besides the diffusive fluxes, there exist several addi- tional pathways for the exchange of solutes across the sedimentwater interface. Convectively driven trans- port of pore water through the interface can occur in shallow waters where shortwave solar radiation pene- trates the water column to the sediment surface and heats the sediment. Similarly, changes in temperature of the water overlaying the sediment surface, e.g., due to internal waves in stratified water bodies, have been observed to drive convective transport across the sedimentwater interface. The existence of larger roughness elements, such as ripples, on permeable sedi- ments can further result in advective pore water exchange driven by pressure differences. Higher dynamic pressure at the upstream side of such topo- graphic structures give rise to the transport of water into the sediment, whereas the lower pressure at the downstream side sucks pore water out of the sediment. Bioturbation and bioirrigation are processes by which benthic fauna or flora enhances the sediment water exchange. Whereas bioturbation mainly refers to the displacement and mixing of sediment particles by, e.g., worms, bivalves, or fish, bioirrigation refers to the flushing and active ventilation of burrows with water from above the sediment surface. These pro- cesses are particularly important in oligotrophic water bodies where the sediment surface remains oxic and provides suitable conditions for a diverse benthic fauna. In more eutrophic systems the emanation of gas bubbles (mainly methane or carbon dioxide) which are formed by biogenic production and a result- ing supersaturation of pore water with these gases may have similar effects. In Situ Flux Measurements The sediment oxygen demand or the release of nutri- ents from the sediment can be of major importance for the overall productivity and for the geochemical composition of a particular water body and quanti- fication of sedimentwater fluxes is often essential for understanding biogeochemical cycles within the water column. As these fluxes depend strongly on the hydrodynamic conditions in the BBL and as these conditions have a strong spatial and temporal dynamics, in situ measurements are often desirable. The measurement of concentration profiles through the sedimentwater interface capable of resolving the diffusive sublayer are one way for estimating the fluxes. From a measured profile of dissolved oxygen, as shown in Figure 6, the sedimentwater flux can be readily estimated by applying eqn [9]. Such measure- ments are carried out using microelectrodes, which are available for a large number of solutes, mounted on a benthic lander system. However, there are two major problems associated with this method: First, although these microelectrodes have tiny tip diameters (down to 10 mm or less for oxygen sensors), they were demonstrated to disturb the concentration distribution within the diffusive boundary layer while profiling. The second and more severe problem results from the complexity of the spatial distribution of the fluxes resulting not only from the small-scale sediment topography (cf. Figure 7) but also from the strongly localized effects of advective pore water exchange and bioturbation. To overcome these pro- blems, the flux can be measured within the turbulent BBL at some distance from the actual sediment sur- face. By neglecting any sources or sinks within the water column between the sampling volume and the sediment surface, this flux represents an areal average of the sedimentwater flux including all non- diffusive flux contributions. The turbulent flux Fturb is determined by the cross-correlation of turbulent vertical velocity (w0 ) and turbulent concentration (C0 ) fluctuations: Fturb w0C0 11 where the overbar denotes temporal averaging. Particle Dynamics BBLs are often characterized by enhanced concentra- tions of suspended particles as compared to the water column above. Such nepheloid layers are generated by resuspension of particles from the sediment sur- face and subsequent upward transport. The potential of a turbulent flow to entrain sediment particles of size D is often described in a Shields diagram where empirical thresholds of sediment motion are provided as a function of a nondimensional shear stress y ru2 =rp rgD and a particle Reynolds num- ber Re uD=n, in which rp is the particle density and g the gravitational constant. The y can be inter- preted as the ratio between the lift force provided by the turbulent shear stress defined in eqn [3] and the gravitational force acting on the particle. While in suspension, the fate of the particle is determined by Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) 237 the balance between upward transport by turbulent diffusion and Stokes settling. The quantitative characterization of resuspension and particle transport, however, is often complicated by cohesive properties of the particles. Cohesive par- ticles require greater shear stresses to become resus- pended; moreover, they tend to form aggregates when in suspension, which alters their settling velocities. The resuspensionsettling cycles increase the con- tact area between particle surfaces and water and thus enhance the fluxes from and to the particles. In addition, suspended particles contribute to water density and locally enhanced resuspension, generated, e.g., by high near-bottom current veloci- ties in the littoral zone or at the depth of the thermo- cline (cf. Figure 1), may lead to the formation of turbidity currents. Glossary Dissipation rate of TKE Rate of dissipation of TKE per unit volume of water and per unit time. This energy is dissipated into heat by internal friction among fluid elements described by viscosity. Nepheloid layer Particle-rich layer above the sediment. This layer is sustained by a balance be- tween gravitational settling and turbulent vertical diffusion counteracting it. Pore water Water that fills the interstitial space between sediment grains. Reynolds number The dimensionless Reynolds number Re is the ratio of inertial to viscous forces acting on a fluid element, obstacle in the flow, or submerged organism and describes the transition from laminar to turbulent flow regimes. Shear stress Force per unit area acting in parallel (tangential) to the surface of a fluid element or interface (e.g., bed shear stress). Turbulent eddies Turbulence is composed of eddies: patches of zigzagging, often swirling fluid, moving randomly around and about the overall direction of motion. Technically, the chaotic state of fluid motion arises when the speed of the fluid exceeds a specific threshold, below which viscous forces damp out the chaotic behaviour (see also Reynolds number). Turbulent kinetic energy Kinetic energy per unit volume of water, which is contained in the random fluctuations of turbulent motions. Turbulent veloc- ity fluctuations u0 can be separated from the mean current velocity u by Reynolds decomposition of the actual velocity u (u u u0 ). Turbulent kinetic energy (TKE) is then defined by, TKE 1=2ru02 , where r denotes density of water. See also: Biological-Physical Interactions; Currents in Rivers; Currents in Stratified Water Bodies 1: Density- Driven Flows; Currents in Stratified Water Bodies 2: Internal Waves; Currents in Stratified Water Bodies 3: Effects of Rotation; Currents in the Upper Mixed Layer and in Unstratified Water Bodies; Density Stratification and Stability; Flow Modification by Submerged Vegetation; Small-Scale Turbulence and Mixing: Energy Fluxes in Stratified Lakes; The Surface Mixed Layer in Lakes and Reservoirs. Further Reading Ackerman JD, Loewen MR, and Hamblin PF (2001) BenthicPelagic coupling over a zebra mussel reef in western Lake Erie. Limnology and Oceanography 46: 892904. Berg P, et al. (2003) Oxygen uptake by aquatic sediments measured with a novel non-invasive eddy-correlation technique. Marine Ecology Progress Series 261: 7583. Boudreau BP and Jrgensen BB (2001) The Benthic Boundary Layer. New York: Oxford University Press. Caldwell DR and Chriss TM (1979) The viscous sublayer at the sea floor. Science 205: 11311132. Gloor M, Wuest A, and Munnich M (1994) Benthic boundary mixing and resuspension induced by internal seiches. Hydrobiology 284: 5968. Gundersen JK and Jrgensen BB (1990) Microstructure of diffusive boundary layers and the oxygen uptake of the sea floor. Nature 345: 604607. Lorke A, Muller B, Maerki M, and Wuest A (2003) Breathing sediments: The control of diffusive transport across the sediment-water interface by periodic boundary-layer turbulence. Limnology and Oceanography 48: 20772085. Lorke A, Umlauf L, Jonas T, and Wuest A (2002) Dynamics of turbulence in low-speed oscillating bottom-boundary layers of stratified basins. Environmental Fluid Mechanics 2: 291313. Lorke A, Wuest A, and Peeters F (2005) Shear-induced convective mixing in bottom boundary layers on slopes. Limnology and Oceanography 50: 16121619. Mellor GL (2002) Oscillatory bottom boundary layers. Journal of Physical Oceanography 32: 30753088. Miller MC, Mccave IN, and Komar PD (1977) Threshold of sedi- ment motion under unidirectional currents. Sedimentology 24: 507527. Wuest A and Gloor M (1998) Bottom boundary mixing: The role of near-sediment density stratification. In: Imberger J (ed.) Physical Processes in Lakes and Oceans. Coastal and Estuarine Studies, pp. 485502. American Geophysical Union. 238 Hydrodynamics and Mixing _ The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs) Currents in Rivers A N Sukhodolov and H-P Kozerski, Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany B L Rhoads, University of Illinois at Urbana-Champaign, Urbana, IL, USA 2009 Elsevier Inc. All rights reserved. Introduction A characteristic feature of fluvial systems is the dis- tinctive directed motion of water masses, or current, caused by gravitational forces. Currents in fluvial systems also differ from other geophysical flows (atmospheric, oceanic, and limnetic) primarily by a presence of irregular flow boundaries, or river chan- nels, developed in bedrock or alluvium. In alluvial channels, cohesive or noncohesive materials are sub- jected to erosion, transport, and deposition, shaping channels by currents and causing alterations in the structure of the currents. For example, nonuniformi- ties in flow structure produce local erosion at banks that with time evolve into the large-scale channel deformations meander bends or loops. Flow curva- ture in bends produces centrifugal forces and coun- teracting pressure-gradient forces, thereby generating helical motion and secondary currents, which enhance channeldeformation. Feedbacks among currents, trans- port of alluvium, and channel deformation result in self-regulating adjustments that dynamically sustain the form of natural fluvial systems. Apart from their significance for processes of ero- sion and deposition, currents in rivers represent an abiotic component of fluvial ecosystems. Flow rates and patterns of currents determine transport and mixing of oxygen, nutrients, and pollutants. More- over, distinctive flow patterns create specific habitats for various forms of aquatic life. On the other hand, biota can substantially influence currents, shaping the structure of habitat to favor conditions for dominant species. A good example is the interaction between biota and flow in vegetated river reaches. Although the qualitative and quantitative assessment of river currents has attracted the attention of scientists for centuries, detailed understanding of these currents has proven elusive due in part to the lack of a general theory of turbulent flows. Therefore, available meth- ods of characterizing river flow quantitatively are based either on case-specific computational models or purely empirical techniques. This article provides an abbreviated overview of the essential physical pro- cesses associated with river currents. The simple case of currents in wide and straight channels is considered first because it provides a theoretical framework and represents the basic (primary) class of currents. Then the effects of nonuniformity in morphology or compo- sition of the riverbed that result in the development of secondary currents are considered along with the effects of channel curvature responsible for the sec- ondary currents of centrifugal origin. Further, compli- cations in the pattern of flow currents are considered using the example of flows through river confluences essential components of river networks. The influence of human actions on river currents in the form of the complex structure of flow around groynes transverse dikes that deflect the flow from erodible banks and promote navigability of river reaches are discussed, followed by analysis of navigation-induced currents generated by commercial vessels. Conceptual and the- oretical principles are illustrated with the examples of original field studies completed by the authors on rivers in Germany and the United States. Controlling Factors and Classifications of Currents Currents in rivers originate at a defined source (chan- nel head or the junction of two streams) and evolve under the mutual influence of gravitational (G) and frictional (F) forces. At the most basic level, currents in rivers can be classified according to whether or not the bulk rate of flow remains constant over time (steady flow) or it changes over time (unsteady flow), and whether or not the bulk rate of flow remains constant over space (uniform flow) or it changes over space (varied flow). In the case of steady, uniform flow, gravitational and frictional forces are equal (G F). However, in unsteady flow, the forces are unbalanced (G 6 F) over time, whereas in varied flow they are unbalanced over space. If G > F the flow accelerates, whereas if G < F the flow decelerates. Motion of water in fluvial systems is a continuous physical process of energy transformation. Potential energy of liquid rgh (where r is density of water, g is gravity acceleration, and h is flow depth) is trans- formed into kinetic energy rU2 (U is bulk flow ve- locity). The ratio between these two forces Fr U= gh p , the Froude number, provides the basis for further classification. The river current can be in a subcritical (Fr < 1), critical (Fr 1), or supercritical (Fr > 1) state. Subcritical flows are typical for low- land rivers and are characterized by smooth, undis- turbed water surfaces. In the critical regime, the surface of the stream develops standing waves, and in supercritical conditions the surface of the water may become distorted into breaking waves. The criti- cal and supercritical regimes are characteristic of 239 mountain torrents and flow around or over engineer- ing structures (dykes, dams), but can also develop in lowland rivers during large floods. Transitions between subcritical and supercritical regimes produce hydraulic drops, or abrupt decreases in flow depth, whereas transitions between supercritical and sub- critical regimes result in hydraulic jumps, or abrupt increases in flow depth. Rivers originate in uplands and flow downhill into lakes, seas, or oceans. Therefore, rivers flow within channels with longitudinal gradients, or slopes (S). The shear stress associated with the gravitational force per unit area oriented along the inclined plane of the channel bed is rghS. A simple expression for the mean velocity of the flow current can be derived from assumptions of uniform flow as: cf ghS/U2 , where cf is a friction factor. This equation can be rearranged as U C hS p , which is known as the Chezy formula and C is the Chezy coefficient. A related empirical formula, U h2/3 S1/2 /n, is known as the ManningStrickler formula and n is the Manning coefficient (C h1/6 /n). It can be seen that the empirical channel resistance coeffici- ents are related to the friction factor as cf g/C2 and cf n2 g/h1/3 . Values of friction coefficients have been determined empirically and are summarized in standard manuals for open-channel flow computa- tions. Values of the Chezy coefficient vary in rivers from 30 to 70, and the Manning coefficient ranges from 0.020 (lowland rivers) to 0.2 (flow over flood- plains with terrestrial vegetation). Although the theory of uniform flow is capable of describing bulk characteristics of currents in rivers, flow in rivers exhibits significant spatial variability because of zero local flow velocity near riverbeds and banks. This variability is a distinctive feature, providing diversity of habitat for aquatic life and is therefore a key factor determining patchiness in the community structure of aquatic organisms and plants communities. The following sections illustrate spatial patterns of currents in rivers and the possibilities of quantifying the processes producing these patterns. Currents in Fluvial Channels Because the permeability of riverbeds and banks is relatively low, velocity at these boundaries can be assumed to be zero. Therefore, velocities in a river cross-section reduce to zero values at the bottom and sides, and are maximal at the surface in the center of the channel (Figure 1). For steady uniform flow not close to the river banks, the gravitational shear-stress compo- nent rghS is balanced by boundary friction causing shear stress within the water column that can be expressed as tz u0w0, where t is shear stress, and u0 , w0 are turbulent fluctuations of velocity in the streamwise and vertical directions, and z is the distance from the riverbed. It can be shown that in uniform flow shear stresses are linearly distributed over the flow depth t t0(1 z/h) with a maximum bed shear stress t0 rghS, at the riverbed. A characteristic velocity scale, shear velocity, can be expressed respectively as U ghS p t0= p . Relating turbulent velocity fluctuations u0w0 to timemean velocity U(z) at certain distance z from the bed provides a simple model of turbulence and allows shear stresses to be expressed as t rnt dU/dz, where nt is turbulent viscosity. This relationship can be integrated to obtain the vertical velocity distribu- tion, but first requires an estimate of nt. The assump- tion of a parabolic distribution of turbulent viscosity over depth, nt Uz 1 z=h p , when substituted into the expression for shear stress, yields a logarith- mic distribution for mean velocity over river depth Uz U In z ks B0 1 where k 0.4 is an universal constant, ks is a charac- teristic height of roughness elements, and B0 8.5 is a constant of integration. Alternatively, eqn [1] can be expressed as Uz U 1 In z z0 2 where z0 exp(ln ks kB0) is hydrodynamic rough- ness parameter. Integrating [2] over river depth pro- vides a logarithmic function expressing the influence of riverbed resistance on the depth-averaged velocity (Ua): C g p Ua U 1 In h z0 1 3 To illustrate the performance of logarithmic law [2], experimental data from some rivers are presented in Figure 2 in nondimensional coordinates z/h exp[Uk/U* ln(h/z0)]. 45 35 25 20 10 20 40 30 10 0cm/s 0 5 m 0.5m 0 Figure 1 Distribution of timemean streamwise velocity in a river cross-section (the Spree River, Germany). 240 Hydrodynamics and Mixing _ Currents in Rivers Secondary Currents So far only the streamwise velocity, or the velocity component parallel to centerline of the channel, has been considered for straight river reaches with uni- form cross-sectional geometry and riverbed material. However, natural stream channels usually meander and exhibit complex morphology and distributions of riverbed material. These variations produce com- ponents to currents that have significant magnitudes perpendicular to the streamwise component. These components, referred to as secondary currents, result in substantial three dimensionality of the overall pat- tern of currents in streams. Depending on their genesis, secondary currents are classified into two categories: secondary currents of first and second kinds. Secondary currents of the first kind are produced by large-scale nonuniformities of channel pattern for example, river bends. Centrifugal forces that develop in a curved channel produce super- elevation of the water surface along the outer bank channel, which generates a counteracting pressure- gradient force. Local imbalances between these forces over the flow depth produce outward motion at the surface, downward motion along the outer bank, and upward, inward motion along the bed (Figure 3). 1 0.8 0.6 0.4 0.2 0 0.01 z/h 0.1 Exp[Uk /U* ln (h/z0)] 1 h, m U, m/s Spree River 1.50 0.35 0.440.35Embarras River 0.500.50Wesenitz River Figure 2 Comparison of measured timemean streamwise velocities over the river depth (symbols) with predicted logarithmic law (line). 20cm/s 0 50m 0 10m 5 cm/s 9 8 7 7 (a) (b) 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 LB RB LB RB 66 Figure 3 Distribution of timemean velocity vectors near the free surface of the flow (a), and (b) secondary currents in the river cross-section, depth is enlarged five times (the Spree River, Germany). Hydrodynamics and Mixing _ Currents in Rivers 241 The resulting pattern of helical motion redistributes momentum shifting the zone of maximum streamwise velocity towards the concave bank near the bend apex (Figure 3). In curvilinear systems of coordinates r (radial), y (tangential), and z (vertical) dynamical equation of flow are presented in the following form: ur @ur @r u r @ur @ w @ur @z u2 r gSr @ @z t @ur @z 4 ur @u @r u r @u @ w @u @z ur u r gS @ @z nt @u @z 5 where ur, uy, and w are radial, tangential, and vertical mean velocities, and Sr, Sy are radial and tangential slopes. Systems [4] and [5] can be solved analytically for the radial component, which represents the second- ary current, if the distributions of tangential velocities and of turbulent viscosity are presented in an ana- lytical form. For natural streams with large radii of channel curvature the distribution of mean velocities usually differs little from the logarithmic law and the parabolic distribution of turbulent viscosity applies t kUz 1 z=h p , then ur 1 2 U h r F1 g p C F2 ; F1 1 0 2ln 1 d; and F2 1 0 ln2 1 d 6 where z/h. Comparison of values predicted with eqn [6] and measured in a typical lowland river mean- der bend show good agreement (Figure 4). The magni- tude of secondary currents of the first kind can be up to 2030% of the magnitude of streamwise velocity com- ponent. These currents are crucial for shaping riverbed relief in channels with loose alluvium. Genesis of secondary currents of the second kind is attributed to the nonuniformity in distributions of roughness or morphology of the riverbed in straight river reaches. These secondary currents have much smaller magnitudes, about 510% of the primary current, and thus are similar to the magnitudes of turbulent fluctuations. Despite their small magni- tudes, these currents are responsible for lateral redis- tributions of fine sediments on the channel bed, forming longitudinal ridges and thus shaping habitats of benthic invertebrates. Some researchers explicitly associate these currents with turbulent structures and use turbulence anisotropy terms as the driving force in models describing the formation of secondary cur- rents in straight river reaches. However, quantitative methods describing such currents are still unavailable because of a lack of knowledge about river turbu- lence, and particularly about coherent structures. Structure of Currents at River Confluences River confluences, or the locations where two rivers join one another, are integral and ubiquitous features of river networks. Currents within confluences are marked by highly complex three-dimensional patterns of flow that include a zone of stagnant, recirculating flow at the upstream corner of the junction of the two rivers, a region of strong flow convergence within the center of the confluence, a shear layer between the merging flows, and in some cases a zone of separated flow near one or both of the banks (Figure 5). It is generally acknowledged that flow structure within confluences is influenced by the junction planform, junction angle, momentum flux ratio, and degree of concordance of the channel beds at the entrance to the confluence. A characteristic pattern of currents within a confluence is the presence of two discrete zones of maximum velocity associated with flow from the two upstream rivers (Figure 6(a) and 6(b)). Between these 1 0.8 0.6 0.4 z/h 0.2 0 4 2 0 V, cm/s 2 4 6 7 eq. (6) 5 Figure 4 Comparison of measured (symbols mark verticals, Figure 3(b)), and predicted (line) timemean radial velocities (the Spree River, Germany). 1 Main stream, 2 Tributary, 3 Stagnation zone 4 Deflection zone, 5 Separation zone, 6 Maximum velocity, 7 Flow recovery zone 53 1 4 6 7 2 Figure 5 Schematic representation of a confluence. 242 Hydrodynamics and Mixing _ Currents in Rivers zones is either a stagnation zone (a region of recirculat- ing, separated flow characterized by negative down- stream velocities) or farther downstream, a shear layer (a zone of intense turbulence along the interface between the converging flows). The most prominent characteristic of the cross- stream velocity fields is the opposing orientation of transverse and vertical velocity vectors on each side the confluence (Figure 6(b)). The magnitudes of the cross-stream vectors reflect the momentum ratio of the two confluent streams with the largest vectors located on the side of the confluence correspond- ing to the dominant tributary. As the flow moves downstream, the two distinct zones of maximum downstream velocity gradually converge. Gradual convective acceleration of flow occurs within the low-velocity region between the two maxima until a uniform downstream velocity field with a single zone of maximum velocity develops downstream of the confluence. A pattern of helical flow, similar to sec- ondary currents of the first kind developing in river bends, can also be present at confluences where curvature of flow from a lateral tributary into the downstream channel generates an effect similar to that which occurs in bends (Figure 6(c)). Although river confluences have been actively stud- ied during the past two decades, the complexity of currents at these locations hinders accurate theo- retical descriptions. Numerical simulation models currently represent the most sophisticated tools for trying to characterize the complexity of river currents at confluences. However, ongoing studies of shallow mixing layers and free recirculating flows suggest that generalized theoretical models may emerge in the next decade. Currents at Engineering Structures Lateral nonuniformity of river currents is associated with natural riverbank protrusions and various engi- neering structures, among which groynes (spur dykes) are the features most widely used to support navigation and protect banks against erosion. Groynes are usually placed in sequences so that the area between successive groynes is referred to as a groyne field. Flow separates at the tip of the protruding groyne, or groyne head, and forms a rotating current in groyne fields depicted by large-scale vortexes with a vertical axis of rotation called gyres. Since water is forced to recirculate within the groyne field in spiraling trajectories, the local resi- dence time for suspended particulate matter can increase substantially and may be sufficient to maintain local phytoplankton reproduction. Therefore, under- standing of these complex currents can have important ecological implications. Specific patterns of flow in a groyne field are con- trolled by the geometry of the field: the aspect ratio between the groyne length (Lg) and the streamwise length of the groyne field (Lf). Observations indi- cate that a two-gyre circulation pattern develops when the aspect ratio is less than a critical value (Lg/Lf < 0.5), and a one-gyre circulation forms in groyne fields aspect ratios greater than the critical value (Lg/Lf > 0.5) (Figure 7). The distribution of mean velocities within the flow in groyne fields can also be reasonably described by a shallow mixing layer model and hyperbolic tangen- tial equation. A canonical free mixing layer (family of free-turbulent flows) evolves in coflowing liquids of different densities or flows of different mean velo- cities, and can be described by a simple model @ @x al 7 U U1 U2 U 2Uc ; U U1 U2 8 1 (a) (b) (c) 1 0 0 4 m 0.4m 0 0.4m 0 2 m0 50cm/s 10cm/s 10m 11 44 100cm/s 2 2 3 3 4 4 Figure 6 Distribution of timemean velocity vectors near the free surface of the flow (a), and (b, c) secondary currents in the river cross-sections (confluence Kaskaskia-Copper Slough, USA). Hydrodynamics and Mixing _ Currents in Rivers 243 where a is the spreading rate (a constant in canonical mixing layer, equals 0.18), d is the width of mixing layer, x is the downstream coordinate, l is the velocity ratio, U1 is the velocity in free part (above) of flow, and U2 is inside the stand, and Uc is the velocity in the centre of the mixing layer. Mean velocity profiles in mixing layers have been shown to comply with a hyperbolic tangential distribution U Us 1 tanh 2y L 9 where Us DU/2, y is the distance across the layer, and L gd is a characteristic length scale normally proportional to the width of the mixing layer. An example of the distribution of depth-averaged veloc- ity across the groyne field and its interface with the mean flow is shown in Figure 8. The specific pattern of recirculation has important implications for distribution of deposited fine sedi- ments within the groyne field. The low-velocity area in the centre of gyres promotes accumulation of rela- tively fine sediments. The thickness of the layer of deposited fines decreases toward the gyre margins, where flow velocities increase. Navigation-Induced Currents Rivers have been always heavily exploited as the inland waterways for commercial and recreational navigation. A vessel moving along a river channel expends energy to overcome resistance of water. The energy is transformed into complex pattern of currents and waves in the lee of the vessel. In width- restricted channels, when commercial tugs towing loaded barges cruise with speed close to the naviga- tional limits, the navigation-induced currents maintain extremely large velocities (Figure 9). An analytical framework for assessment of such currents was deduced from the balance of kinetic energy and repre- sented by a relationship 0 (a) (b) 25 50m 100cm/s Figure 7 Distribution of depth-averaged timemean velocity vectors (interpolated from measurements) in the groyne field with aspect ratio (a) 0.6, and (b) 0.4 (the Elbe River, Germany). 1.0 0.5 0.5 0.5 0.0 0.5 1.0 0.0 U/Umax y/Lg Field data (Elbe) Laboratory data Hyperbolic tangent approximation Figure 8 Measured distributions of depth-averaged timemean velocities (section through the gyre center) in the mixing layer between main flow and groyne field, and their approximation with hyperbolic tangent (eqn [10]). 244 Hydrodynamics and Mixing _ Currents in Rivers U U0 a0 h0 h r exp b y B h i 10 where a0 and b are parameters depending on the char- acteristics of kinetic energy transfer (dispersion coeffi- cient, wave celerity, and channel width B), U is maximal value of depth-averaged velocity in naviga- tion-induced current, U0 is the speed of the vessel, h is the flow depth, h0 is the draught of the vessel, and y is the transverse distance from the vessel towards waterway bank. Performance of the relation [10] is illustrated in Figure 10, where the results of field mea- surements are compared with values predicted by the model [10]. Conclusions The major factors controlling currents in rivers are the macro- and microscale geometry of the river channel, the joining of streams induced by the structure of fluvial networks, properties of alluvium composing the riverbed material, biological features, and anthro- pogenic influences. Although quantitative descriptions of currents in rivers are based on well-known theoreti- cal principles, a universal theory of river currents has yet to be developed mainly because of the lack of a universal theory for turbulence aspects of river flows. The problem of quantitative description is presently solved with application of case-specific models and relies substantially on the application of empirical knowledge. Mutual interactions among flow, the river channel, and biota at different spatial and temporal scales ranging from a sediment grain to the scale of a river reach, and from milliseconds to hundreds of years complicate unambiguous studies of currents. Therefore, available data on important parameters in models of river currents include significant scatter that leads to uncertainties in prediction of magnitudes and patterns of flows. Some of this uncertainty reflects the fact that most theoretical, laboratory, and field studies investigate or assume uniform steady flow, while in nature such flows are always an idealization. Nomenclature B width of a channel (m) B0 integration constant C Chezy coefficient (m1/2 s1 ) cf friction factor F friction force (kg m s2 ) Fr Froude number F1, F2 integral functions G gravity force (kg m s2 ) g gravity acceleration (m s2 ) h mean depth (averaged over cross-section) (m) h0 draught of a vessel (m) ks height of roughness elements (m) L length scale (m) Lg length of groyne (m) Lf length of groyne field, m n ManningStrickler coefficient (m1/3 s) r radial coordinate (m) S longitudinal gradient of the water surface Sr radial slope Sy tangential slope U timemean velocity (m s1 ) Uc timemean velocity in the centre of the mixing layer (m s1 ) U0 cruising velocity of a vessel (m s1 ) u0 streamwise velocity fluctuations (m s1 ) ur radial mean velocity (m s1 ) 80 60 40 20 0 20 40 0 40 80 Time, s Velocity,cm/s 120 160 200 Figure 9 Navigation-induced current from a towing barge measured 15 cm above the riverbed at 2 m distance from the water edge (Oder-Havel Canal, Germany). 2.0 1.6 1.2 0.8 0.4 0.0 0.0 0.2 0.4 0.6 0.8 1.0 y/B Uh0.5/U0h0 0.5 Figure 10 Measured (circles) and predicted (line) values of return currents. Hydrodynamics and Mixing _ Currents in Rivers 245 uy tangential mean velocity (m s1 ) U* shear velocity (m s1 ) Us mean velocity half of velocity difference in mixing layer (m s1 ) U1, U2 velocity in fast and slow flows (m s1 ) w0 vertical velocity fluctuations (m s1 ) y transverse distance (m) z vertical coordinate (m) z0 hydrodynamic roughness parameter (m) DU velocity difference (m s1 ) a spreading rate a0 parameter b parameter g dimensionless coefficient d width of the mixing layer (m) dimensionless distance y tangential coordinate (grad.) k von Karman parameter l velocity ratio nt turbulent viscosity (m2 s1 ) r density of water (kg m3 ) t shear stress (kg m1 s2 ) t0 bottom shear stress (kg m1 s2 ) See also: Flow in Wetlands and Macrophyte Beds; Flow Modification by Submerged Vegetation. Further Reading Cunge JA, Holly FM Jr, and Verwey A (1980) Practical Aspects of Computational River Hydraulics. London: Pitman. Best JL and Reid I (1984) Separation zone at open-channel junc- tions. Journal of Hydraulic Engineering 110: 15881594. Ghisalberti M and Nepf H (2002) Mixing layers and coherent structures in vegetated aquatic flows. Journal of Geophysical Research 107(C2). doi 10.1029/2001JC00871. Gordon ND, McMahon TA, and Finlayson BL (1992) Stream Hydrology: An Introduction for Ecologists. Chichester: Wiley. Leopold LB (1994) A View of the River. Cambridge: Harvard University Press. Nezu I and Nakagawa H (1993) Turbulence in Open-Channel Flow. Rotterdam: Balkema. Rhoads BL and Sukhodolov AN (2001) Field investigation of three- dimensional flow structure at stream confluences: 1. Thermal mixing and time-averaged velocities. Water Resources Research 37(9): 23932410. Rozovskii IL (1961) Flow of Water in Bends of Open Channels. [trans.]. Jerusalem: Israel Program for Scientific Translations. Schlichting H and Gersten K (2000) Boundary Layer Theory. Berlin: Springer. Sukhodolov AN, Uijttewaal WSJ, and Engelhardt C (2002) On the correspondence between morphological and hydrodynamical patterns of groyne fields. Earth Surface and Landforms 27: 289305. Sukhodolov AN and Sukhodolova TA (2006) Evolution of mixing layers in turbulent flow over submersible vegetation: field experi- ments and measurement study. In: Ferreira RML, Alves ECTL, Leal JGAB, and Cardoso AH (eds.) RiverFlow2006, pp. 525534. London: Balkema. Wolter C, Arlinghaus R, Sukhodolov AN, and Engelhardt C (2004) A model of navigation-induced currents in inland waterways and implications for juvenile fish displacement. Environmental Man- agement 35: 656668. Yalin MS (1992) River Mechanics. Oxford: Pergamon. Relevant Websites Center for Water as a Complex Environmental System (CWACES), Urbana-Champaign, Illinois, USA. WL|Delft Hydraulics, the Netherlands. National Center for Earth-surface Dynamics, Minneapolis, USA. National Institute of Water and Atmospheric Research, New Zealand. Institute for Hydromechanics in Karlsruhe, Germany. Institute of Freshwater Ecology and Inland Fisheries, Germany. 246 Hydrodynamics and Mixing _ Currents in Rivers Currents in Stratified Water Bodies 1: Density-Driven Flows F Peeters, Universita t Konstanz, Mainaustrasse, Konstanz, Germany R Kipfer, Swiss Federal Institute of Environmental Science and Technology (Eawag), Swiss Federal Institute of Technology (ETH), Ueberlandstr, Duebendorf, Switzerland 2009 Elsevier Inc. All rights reserved. Introduction Vertical transport of dissolved substances and heat in lakes mainly results from two different mechanisms: (a) mixing by turbulence that is usually described as a diffusive transport and (b) density-driven exchange that can be considered as an advective transport. A typical example of the latter is convection owing to surface cooling in fall, which often leads to iso- thermal conditions in shallow lakes of the temperate zone. Because entrainment of ambient water limits the depth of convective plumes, density-driven trans- port to large depth in deep lakes usually occurs along the lake boundaries and is often the result of specific and localized processes, which are discussed later. The important role of density-driven transport for vertical exchange in lakes becomes evident if one considers that temperature stratification typical for most lakes is characterized by a decrease in water temperature with increasing water depth. Turbulent diffusion causes heat to flow from high to low temperatures and hence typically leads to a gradual continuous warming of cold deep-water regions. Thus, on a long-term average, advective processes transporting cold surface water downwards must be sufficient to compensate for the heat flux due to turbulent diffusion. The low temperatures in the deep water are usually either the remnant of isother- mal conditions generated by buoyancy-driven over- turn during the cold season or originate from cold density currents propagating to largest depth. Because vertical transport due to density currents plays an important role in overall deep-water renewal and heat exchange, density driven exchange processes are central to the understanding of oxygenation and nutrient transport especially in deep lakes. In the worlds largest and deepest water bodies sev- eral processes have been identified that lead to advec- tive deep-water renewal by density currents: river inflow, e.g., in Lake Constance, Lake Geneva, and Lake Baikal; inter-basin exchange, e.g., in Lake Lucerne, Lake Baikal, or even in the Caspian Sea; differential cooling, e.g., in Lake Geneva, Lake Con- stance, Lake Issyk-Kul, and Lake Malawi; thermal-bar mixing, e.g., in the Lake Ontario, Lake Ladoga, Lake Michigan, and Lake Baikal; and transport due to thermobaric instabilities, e.g., in Lake Baikal and possi- bly in Crater Lake. All these processes have been shown to significantly contribute to deep-water renewal in lakes, although advective transport to the lake bottom was not conclusively demonstrated in all cases. More details on the different processes are given below. In the following, we first describe the principal characteristics of density currents and the associated signals of intrusions in vertical profiles of water constituents and temperature. Then, we present several mechanisms that lead to the generation of density plumes in deep freshwater lakes and discuss which of these processes can also be responsible for deep-water renewal in tropical and saline lakes. Finally, we discuss the potential impact of changes in the catchments of lakes and in the meteorologi- cal conditions on deep-water renewal by density currents. Characteristics of Density Currents Density currents are driven by differences in water density, which can result from gradients in water tem- perature, salinity, dissolved uncharged substances, or suspended particles and are also affected by pressure. If a water mass with higher density is situated above a water mass with lower density, the stratification is unstable and buoyancy causes the upper water mass to sink. In the sinking process ambient water is mixed into the sinking water mass and thus alters its density (Figure 1), thereby reducing the density difference between the density plume and the ambient water. Furthermore, the properties of the ambient water change along the path of the sinking water mass. Hence the buoyancy of the sinking plume changes continuously as it sinks into deeper depth. Eventually, a depth is reached where the density of the density plume and the density of the surrounding water become equal. At this depth the sinking process ceases and the plume water spreads out laterally into the ambient water forming an intrusion (Figure 1). In many cases the sinking plume meets the lake bound- ary and then continues to sink along the lake boundary (Figure 1). In this case, entrainment of ambient water is limited to the upper side of the density plume and less ambient water is entrained per unit sinking depth. Hence the characteristic properties of the water within the density plume (e.g., temperature, salinity, suspended particles, dissolved oxygen) change more 247 slowly and the density plumes typically can propagate to larger depths than would be possible in the open water. The occurrence of density plumes propagating from shallow to deep water are indicated by intru- sions that can be identified in CTD-profiles (conduc- tivity as measure of salinity, temperature, and depth) and in profiles of dissolved substances and suspended particles. Figure 2 presents an example from Lake Issyk-Kul (Kyrghystan), where intrusions are charac- terized by a higher dissolved oxygen concentration and a lower light transmission than is observed in the ambient water. High oxygen levels in the intrusions indicate oxygen-rich surface water that must have been trans- ported recently because oxygen levels have not yet been significantly reduced by degradation processes. The low light transmission in the intrusions indicates water with a high load of suspended particles suggest- ing either, that the water that generated the density current was enriched in suspended particles and thus may have originated from river inflow, or, that the density plume responsible for the intrusions has pro- pagated along the lake boundary and caused resus- pension of sediments during the sinking process. Temperature is usually not a good indicator of intru- sions because it is a key parameter determining plume density. Thus, at the depth of the intrusion, plume water and surrounding water often have about the same temperature. However, in cases where the den- sity plume propagates down to the largest depths, as it is sometimes the case e.g., in Lake Baikal, tempera- ture anomalies at the lake bottom can be used to identify density plumes. Temperature Density Figure 1 Schematic illustration of density currents. The shading on the left-hand side of the figure indicates an increase in density with increasing depth. 0 200 400 Depth(m) 600 4.3 4.5 Potential temperature (C)(a) Salinity (g kg1 ) Dissolved oxygen (mg l1 ) Light transmission (%) 4.7 4.9 6.002 6.004 6.006 8 9 10 80 81 82 83 Figure 2 Intrusions as indicators of density currents. Vertical profiles of temperature, salinity, dissolved oxygen, and light transmission measured in Lake Issyk-Kul. The distinct features in these profiles suggest intrusions from density currents. Grey bars mark depth regions with high concentrations of dissolved oxygen and low light transmission, suggesting water originating from shallower depth regions. Redrawn from Figure 2 in Peeters FD, Finger M, Hofer M, Brennwald DM, and Livingstone R Kipfer (2003). Deep-water renewal in Lake Issyk-Kul driven by differential cooling. Limnology & Oceanography 48(4): 14191431. 248 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows Density Plumes Generated by External Inputs River Inflows The density differences required to drive density plumes originate from processes that generate hori- zontal or vertical gradients in water properties. An obvious example is river inflow (Figure 3). River water usually contains an increased load of suspended particles and has a different temperature and salinity than the lake water. Hence, river inflow is commonly associated with density plumes propagat- ing from the river mouth to larger depths. The kinetic energy associated with the inflow of the river water is usually rapidly dissipated and the horizontal den- sity gradients resulting from the different densities of river water and lake water are the main cause of river induced transport of water masses in lakes. During summer, the density plumes induced by river inflow typically intrude at some depth within the thermo- cline of freshwater lakes. Because of the large temper- ature gradients in the thermocline, water densities change significantly within a rather narrow depth range in the lake. Hence, the probability that the density of the plume water agrees with the density in the water column of the lake is especially large within the thermocline. This fact explains that river water typically intrudes in this depth range. The depth reached by the density plumes varies during the course of the year since water properties and hence the density of lake and river water changes seasonally (Figure 3). Density currents containing a high load of Lake Brienz Aare Aare Aare (a) Ltschine 50 100 150 Depth(m) 200 250 2 4 6 Distance from Ltschine mouth (km) 8 10 12 2 4 6 Distance from Ltschine mouth (km) 8 10 12 1.0 c (gm3) c (gm3) 1.1 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 1.0 1.5 2.0 2.5 3.0 4.0 6.0 8.0 10.0 15.0 (b) (c) Ltschine Figure 3 Density currents generated by river inflow. (a) Water of river Aare indicated by high turbidity intruding near the surface of Lake Brienz. The sharp boundaries of this surface plume indicate plunging of river water to larger depth. (b, c) Suspended particle distribution inferred from light transmission measurements in a longitudinal cross-section of Lake Brienz measured in February (b) and October (c). The particle distributions suggest that, in February water introduced by the river Aare (inflow on the right-hand side) sinks as density plume along the lake bottom towards largest depth (b). In October river Aare and river Lu tchine both intrude at intermediate depth (c). (Figure 3(a) was provided by Ueli Ochsenbein; Figure 3(b) and (c) are redrawn from Figure 7(a) and 7(d) in Finger D, Schmid M, and Wu est A (2006). Effects of upstream hydropower operation on riverine particle transport and turbidity in downstream lakes. Water Resources Research 42, W08429, doi:10.1029/2005WR004751. Reproduced/modified by permission of American Geophysical Union. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows 249 suspended particles are often called turbidity cur- rents. Sedimentation of particles out of intrusions resulting from turbidity currents can reduce the den- sity of the intruding water sufficiently that the depth of the intrusions becomes shallower over time. Den- sity currents induced by river inflows usually propa- gate along the sloping bottom boundary before the water intrudes laterally. If the concentrations of solutes and particles are very different between the river and the lake water, the plumes can propagate down to the deepest parts of the lake. In cases where the sinking water is confined to underwater channels, e.g., density plumes propagating down the Kukui Canyon of the Selenga delta in Lake Baikal, entrain- ment of ambient water is reduced, and the density plume can propagate over a depth range of more than 1000 m down to 1640 m (see also Figure 4(a)). Interbasin Exchange River inflows not only result in localized density plumes propagating from the river mouth to larger depths but also can generate subtle large scale gradi- ents in water properties that affect the horizontal density distribution on a basin scale. These small density gradients on a large spatial scale may contrib- ute to the generation of density currents far from the river inflow that occur especially in the vicinity of sills separating sub-basins of the lake. This mechanism is exemplified in Figure 4 for two lakes of different size, Lake Baikal and Lake Lucerne, that both are structured into several sub-basins separated by sills. In both lakes large scale horizontal salinity gradi- ents are generated by river inflows introducing water with different ion concentrations into the different sub-basins. In the case of Lake Baikal, the River Selenga introduces more saline water into the Central Basin than the Upper Angara River introduces into the Northern Basin. In case of Lake Lucerne, the River Sarner Aa introduces more saline water into the sub-basin Lake Alpnach than the River Reuss introduces into the sub-basin Lake Uri. Because of the salinity gradients, the density of the water in the different sub-basins differs if temperature is the same. In Lake Lucerne the densest water can be found in sub-basin Lake Alpnach when winter cooling reduces surface water temperature to $4 C. Horizontal trans- port of the dense water from Lake Alpnach to the sub- basin Lake Vitznau across the sill separating the two sub-basins induces a density current renewing the deep-water of sub-basin Lake Vitznau (Figure 4(b)). The density plume causes upwelling of cold dense water within Lake Vitznau. Horizontal transport of water across the sills between sub-basin results into a cascading of density driven transport within all sub-basins (Figure 4(b)). A similar process is operating in the different basins of Lake Baikal (Figure 4(a)). Prerequisite of these density currents generated at sills between sub-basins is (1) the structuring of the lake basin into sub-basin that prevents homogenization of water properties by horizontal mixing and (2) a hetero- geneous input of water properties, as e.g., the salinity by the river inflows in Figure 4. 0 400 800 Depth(m)Depth(m) 1200 1600 0 100 200 0 10 20 Relative distance (km)(b) 30 40 0(a) 200 248 158 162 165 155 158 152 148 162 400 600 95.2 95.2 95.0 95.0 Southern basin Central basin Selenga delta Northern basin Academician ridge Lake Vitznau Lake Lucerne Lake Alpnach Lake Gersau Lake Uri Lake Baikal 95.4 95.2 95.0 94.7 94.5 94.3 94.5 94.7 Figure 4 Density currents generated at sills between sub-basins. Vertical transects of salinity in Lake Baikal (a) and in Lake Lucerne (b). In both lakes the horizontal gradients in salinity are generated by river inflows introducing water with different ion concentration. The salinity distributions suggest that density currents are not only generated directly by river inflow as is the case in Lake Baikal at the Selenga delta (see panel a) but that density currents also occur in both lakes at the sills between sub-basins most likely driven by horizontal transport across the sill. Contours depict salinity in mg kg1 . Figure 4(a): redrawn from Kipfer R and Peeters F (2000). Speculation on consequences of changes in the deep water renewal in Lake Baikal, in K Minoura (ed.) Lake Baikal a mirror in time and space for understanding global change processes, pp. 273280. Amsterdam, Netherlands: Elsevier. Figure 4(b): drawn using data from Aeschbach-Hertig W, Kipfer R, Hofer M, Imboden DM, and Baur H (1996) Density-driven exchange between the basins of Lake Lucerne (Switzerland) traced with the 3 H-3 He method. Limnology and Oceanography 41: 707721. 250 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows Subsurface Inflows Besides the input from rivers, external water sources derived from groundwater inflows and from hydro- thermal vents can generate density currents depend- ing on the depths at which the inflows are located. Ground water and hydrothermal water is usually highly enriched in ions and thus can cause salinity driven density plumes. Groundwater inflows into lakes are common in artificial lakes such as mining lakes or gravel-pit lakes or occur in karstic environ- ments. Density currents due to hydrothermal vents have been reported for instance in Lake Baikal, where hydrothermal water is introduced in Frohliha Bay at a depth of 200400 m and propagates as a bottom following density current down to 1400 m depth. In this specific case the salinity of the hydro- thermal water is sufficiently large to compensate the decrease in density due to the increased water tem- peratures in the hydrothermal water. Density Plumes Generated by Internal Processes Differential Cooling A key parameter affecting water density is tempera- ture. However, for density currents to be induced on the basis of the temperature of water, horizontal gra- dients in temperature are required. Horizontal tem- perature gradients are generated by external surface and subsurface inflows (see earlier text) but also by internal processes. In most lakes the heat flux at the lake surface (expressed per unit area) can be consid- ered as horizontally homogeneous because meteoro- logical parameters and radiation do not vary significantly at the length scale of the lake basin. Nevertheless, differential cooling can generate signif- icant temperature differences within lakes and thus generate density currents (e.g., Wellington Reservoir, Lake Geneva, Lake Constance, Lake Banyoles). Heat loss at the lake surface causes vertical convection and thus mixing of surface water with water from layers below. This process continuously mixes the cooled surface water with water from deeper layers contain- ing heat stored during the warm season. In shallow- water regions, the reservoir of warmer deep water is exhausted earlier than in regions with large water depth. Hence, in shallow-water regions heat loss at the lake surface leads to a faster cooling of the water column than in deep-water regions. Because the cold water in the shallow-water regions has a larger den- sity than the warmer water in the pelagic, deep-water regions, the cold water propagates downwards as a density current. Such density plumes often occur only sporadically. They are typically generated during night-time cooling in fall as has been demonstrated in e.g., Lake Constance and Lake Geneva (Figure 5) or during events that also induce cooling such as cold fronts or monsoons. Differential cooling can result in density driven currents from any shallow region in a lake basin. Therefore it may affect a large volume of water and thus may significantly contribute to overall vertical transport. The process is particularly effective if large shelf regions are located around a deep basin. The density currents induced by differential cooling prop- agate along the lake bottom and can reach large depths especially if channels exist along which the density current can propagate without significant entrainment of ambient water, as is the case e.g., in Lake Issyk-Kul. Note, that in freshwater lakes dif- ferential cooling can only generate density plumes if water temperatures are above the temperature of maximum density (Tmd) which is about 4 C at the lake surface. Cooling below Tmd implies a decrease in water density and thus prohibits density plume devel- opment by differential cooling. Hence, in freshwater lakes the temperature of density plumes associated with differential cooling is at least 4 C or higher. Thermal Bar Temperature-driven density currents can also result from horizontal mixing of two adjacent surface water masses, one having a temperatures above and the other below Tmd. Because of the non-linear temperature 0 50 100 Depth(m) 150 0 500 1000 1500 Distance (m) 2000 6.20 6.16 6.22 6.24 6.12 2500 Figure 5 Density current generated by differential cooling. Contour lines represent isotherms in C indicating a density plume generated by differential cooling in Lake Geneva. Note that the temperatures are well above 4 C. The isotherms are constructed from CTD-data collected at the locations indicated by the arrows. Redrawn from Figure 2(b) in Fer I and Lemmin U. Winter cascading of cold water in Lake Geneva. Journal of Geophysical Research 107, NO. C6, 10.1029/2001JC000828, 2002. Reproduced/modified by permission of American Geophysical Union. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows 251 dependence of the equation of state, mixing of water masses with different temperatures always results in an increase in the mean density of the water. This process is called cabbeling. If the temperature of the mixed water is closer to the Tmd than the water below, it sinks as a density plume. A so-called thermal bar devel- ops which is characterized by a vertically isotherm water column with a temperature close to Tmd separat- ing an open water region with temperatures below Tmd from a warmer shore region with temperatures above Tmd (Figure 6). The downward flow of dense surface water at the thermal bar can cause significant renewal and oxyge- nation of deep water. As time progresses the thermal bar moves further away from the shore to the open water. The dynamics of this process depends on the morphometry of the lake and on the atmospheric forc- ing. Mixing associated with the thermal bar has been 20 2 4 4 6 6 8 8 2 2 2 4 8 6 2 2 2 12 12 10 2 24 May 92 4 4 4 6 8 6 8 8 N 16 May 92 Isobath in m (a) (b) (c)0 4 4 4 4 6 4 4 6 8 14 12 10 14 16 18 10 8 6 4 6 (f) 10 12 5 9 810 10 12 10 (d) (e) (g) 4 8 8 50 3 Jun 92 9 Jun 92 28 Jun 92 100 km 80 60 40 20 20 40 100 60 (h) 3 5 7 Surface temperature (C) 9 11 Figure 6 The thermal bar. The development of a thermal-bar in Lake Ladoga indicated by surface temperatures measured with satellites (af ) and the observation of a thermal bar near Selenga delta in Lake Baikal (g and h). Panel (a) provides the morphometry of Lake Ladoga with depth contours given in m. Panels (bf) depict surface temperatures with isotherms in C. Panels (bf) show how the thermal bar, which is located at the 4 C isotherm, moves towards deeper water as the season progresses. The position of the thermal bar changes more rapidly in the gently sloping shallower south-eastern part of the lake than in the steep and deep northern part. In (g), the sharp boundary between near shore water and open water indicates the position of the themal bar located near the Selenga delta in Lake Baikal. The color differences result from differences in the load of suspended particles. The water trapped near shore by the thermal bar has an increased load of suspended particles owing to the nearby inflow of the Selenga River. Panel (h) shows an image of the surface temperatures near Selenga delta derived from satellite data. Density currents are generated at the sharp transition between warm shore water and cold open water characterized by a temperature close to 4 C. White areas are land. Figure 6(af) are redrawn from Figures 1 and 3 in Malm J, Mironov D, Terzhevikl A, and Jiinsson L (1994) Investigation of the spring thermal regime in Lake Ladoga using field and satellite data. Limnology and Oceanography 39(6): 13331348. Copyright 2000 by the American Society of Limnology and Oceanography, Inc. 252 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows reported for Lake Ontario, Lake Ladoga, Lake Michi- gan, and Lake Baikal. Because the thermal bar requires open-water temperatures below Tmd, it occurrs mainly in lakes which become ice covered in winter. The horizontal temperature gradients required for thermal bar development are generated by differen- tial heating during spring warming, a process similar to differential cooling. Initially in spring, when sur- face-water temperatures are below Tmd, an increase of water temperature during spring warming leads to an increase in the density of the surface waters and thus to convection. Because convection mixes the warmer surface water with colder water from below and the reservoir of the cold water from below is smaller in shallow near-shore than in deeper open- water regions the temperature in the shallow-water regions increases faster than in the deep off-shore regions. When the temperature in the shallow regions exceeds 4 C the water column is stratified and fur- ther influx of heat is not connected to convection, but leads to an even faster increase in the water tempera- ture. Thus, a horizontal temperature gradient typical for a thermal bar situation develops with tempera- tures below Tmd at the surface of the open-water region and temperatures above Tmd at the surface in the shallow near-shore regions. A reverse thermal bar situation with temperatures below Tmd in the shallow-shore region and temperatures above Tmd in the open-water region could develop in fall as a consequence of differential cooling if cooling in the shore region progresses to temperatures below Tmd. However, in the case of the reverse thermal bar exchange processes will be dominated by horizontal density gradients below the surface (see the section on Differential cooling). Thermal Baricity Another process that can generate density plumes as a consequence of the nonlinearity of the equation of state of fresh water is the thermobaric effect. The thermobaric effect results from the fact that Tmd decreases with increasing pressure. The generation of density currents by the thermobaric effect requires a very specific temperature stratification that occurs only in few stably stratified deep freshwater-lakes, e. g., Lake Baikal or Crater Lake. To generate density currents by the thermobaric effect, water tempera- tures must be below 4 C throughout the water col- umn. The temperature in the surface layer must increase with increasing depth, whereas the tempera- ture in the deep-water must decrease with increasing depth. Then, the temperature profile has a maximum at intermediate depth, the so-called mesothermal maximum (Figure 7). A water column with such a temperature profile is stably stratified because of the effect of pressure on fresh water density. If the water column is displaced downwards or pressure is increased, the temperature at the mesothermal maximum is higher than the local Tmd and the water column becomes unstable. Cold water from above the mesothermal maximum can sink downwards as a density plume (Figure 7). Simi- larly, a water mass from the cold upper layer can be pushed downwards below the mesothermal maxi- mum to a depth where its temperature is closer to Tmd than the temperature of the ambient water. Then, it will continue to sink driven by its buoyancy until the surrounding water has the same temperature as the sinking water mass. Besides the specific temper- ature profile in the water column the exchange due to the thermobaric effect also requires a mechanism by which the water pressure is altered substantially and/or the water is locally pushed downwards across the depth of the mesothermal maximum. Hence density plume generation by the thermobaric effect is not very common. Several investigations have claimed that the thermobaric effect may be important for deep-water oxygenation in Lake Baikal. However, the mechanism that could cause the required downward displacement in the open water column remained unclear. Recently, wind-driven Ekman transport near the coast of the 0 200 400 Tmd 600 Depth(m) 800 2.8 3.0 3.2 Temperature (C) 3.4 3.6 Figure 7 Schematic on the generation of density currents by the thermobaric effect. The temperature profile presented has been measured in the northern basin of Lake Baikal. The temperature of maximum density as function of depth shown for comparison is labelled with Tmd. Vertical displacement of the temperature profile (indicated by the dashed line) leads to a density driven vertical transport that is self supporting over the depth range indicated by the arrow. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows 253 Southern Basin of Lake Baikal has been suggested to cause thermobaric instabilities. Turbidity Currents Generated by Waves Internal processes not only can generate temperature gradients but also can cause gradients in suspended particles that are sufficient to drive density currents. Shear stress at the lake bottom associated with sur- face waves and high-frequency internal waves can induce sediment resuspension and thus increase the load of suspended particles in the water column. If the density increase induced by the change in particle load is sufficiently large to compensate vertical den- sity stratification, turbidity currents are generated. Because the turbidity gradient is generated by the interaction of waves with the sediment, the resulting turbidity currents usually originate either near the shore at the lake surface (surface waves) or at the depth of the thermocline (high-frequency internal waves). The turbidity currents usually propagate along the lake bottom to larger depth until they intrude into the open water. Horizontal Density Currents Generated under Ice Cover Temperature-driven density currents can also occur under ice cover due to differential heating by solar radiation. This process is invoked if the optical prop- erties of the ice and snow cover vary horizontally either due to a variation in the ice structure (e.g., white ice and black ice) or in the thickness of snow cover. Then, penetration of solar radiation through the ice and snow cover varies horizontally and thus induces differential heating in the surface water below the ice. This process causes convection below the ice and results in horizontal density gradients that can drive horizontal density currents. Such under-ice currents are believed to be essential for the develop- ment of algal blooms in early spring in Lake Baikal. Density Currents in Tropical and Saline Lakes In tropical lakes and also in saline lakes several of the processes mentioned above do not occur. Because the development of a therma bar requires a lateral transi- tion of water temperature from above to below Tmd at the lake surface, a thermal bar never occurs in tropical lakes where water temperatures are above 4 C all year round and thus always exceed Tmd. Because Tmd decreases with increasing salinity reaching freezing temperature at about 25 g kg1 , thermal bar development and the associated density currents also do not play an important role for the vertical exchange in saline lakes. The same arguments exclude the thermobaric effect as a significant cause of density currents in tropical and saline lakes. In tropical lakes temperature gradients play the dominant role in the generation of density currents because at high water temperatures, slight tempera- ture gradients imply large differences in density. Therefore, salinity gradients play a smaller role for density plume generation in tropical lakes than for lakes of temperate regions during the cold season. Convection due to night-time cooling and density currents due to differential cooling and river inflows can be expected to be the most important processes for advective deep-water renewal in tropical lakes. In saline lakes, however, river inflows usually can- not drive density currents because rivers typically introduce fresh water that in most cases has a much lower density than the saline lake water, even if the inflow has a low temperature. For example water with a salinity of 4 g kg1 and a temperature of 24 C has a greater density than fresh water with 4 C. Hence, river inflows can only directly drive density currents in saline lakes, if the riverine water carries a substantial load of suspended particles. Nev- ertheless, in saline lakes river inflows can generate large scale differences in salinity and thus may indi- rectly lead to density currents at sills induced by inter basin exchange as is probably the case in the Caspian Sea. Another process that is likely to cause density currents in saline lakes is differential cooling. In con- trast to freshwater lakes this process can trigger den- sity currents with temperatures well below 4 C and even down to freezing temperature, because Tmd can be substantially reduced or even does not exist depending on the salinity of the water. Impact of Changes in the Environmental Conditions on Density Currents and Deep-Water Renewal Changes in climatic conditions and human activities in catchments may affect density currents and thus vertical mixing in lakes. An increase in precipitation and in the percentage of the land made impervious by human development typically leads to a higher dis- charge of rivers. Enhanced river discharge is usually associated with increased erosion and a higher load of suspended particles in the river water such that density currents will propagate to larger depth. Enhanced deep-water renewal is thus anticipated in freshwater lakes. In saline lakes, however, the increase in fresh water input associated with increased precipitation reduces the density of the 254 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows surface waters and thus can significantly limit the generation of density currents. Consequently, deep- water renewal may be reduced or suppressed. Deep- water exchange decreased drastically as a conse- quence of increased riverine discharge in the Caspian Sea and in Mono Lake, CA. Water storage dams in the catchments of lakes have the opposite effect on density currents than soil seal- ing. Retention by water storage dams reduces peak discharge and the load of suspended particles in downstream rivers. This results in a decrease in the intensity of density currents and in the depth of intru- sions in lakes located downstream of dams. Climate warming can lead to a reduction of deep- water renewal in lakes because additional input of heat at the lake surface may result in an increase in density stratification of the water column and in an extension of the stratified period. Persistence of the increased stratification over many years likely depends on the lakes latitude and depth and whether warming is intensified in winter or summer or, for tropical lakes, during the monsoon period or during less windy periods. In a warmer climate, however, mixing in freshwater lakes due to density currents associated with the ther- mal bar and/or the thermobaric effect may cease, if climate warming leads to an increase in surface water temperature to values above 4 C all year round, i.e., to values above Tmd. Because density is a nonlinear function of temperature, warming of surface water may also shift the relative importance of turbidity and salinity gradients towards temperature gradients as agent to drive density plumes. The potential consequences of environmental change on density currents are exemplified for Lake Baikal, the deepest lake on earth. Because of the peculiar temperature profile with the mesothermal tempera- ture maximum (see Figure 7), deep-water renewal in Lake Baikal is predominantly driven by salinity dif- ferences between river and lake water and between the basins of the lake. The salinity differences result in density plumes associated with riverine inflows and inter-basin exchange. Hence, changes in the catch- ments leading to an increase in the concentration of dissolved ions and suspended particles in river inflow will intensify deep-water mixing by density plumes. Climate warming on the other hand will not severely affect density plumes and thus deep-water renewal in Lake Baikal, as long as the lake has an annual ice cover. Higher air temperatures most likely result in a shift of ice break-up to earlier times in the year, but will not have an affect on the thermal conditions immediately after ice break-up. Hence, the conditions required to generate density plumes will not change, but may occur earlier in the season. In summary, density currents significantly contrib- ute to deep renewal, especially in deep and very deep lakes. The density currents can result from a variety of processes. Which of these processes are relevant in a specific lake depends on the temperature regime of the lake, its salinity and also its morphometry. The environmental conditions, e.g., precipitation in the catchments and heat flux at the lake surface affect the occurrence of density currents and the depth reached by the density plumes. Hence, changes in the environmental conditions will have consequences for deep-water renewal and oxygenation of deep lakes not only because of a change in turbulence levels, but also by their effect on the intensity of density currents. See also: The Benthic Boundary Layer (in Rivers, Lakes, and Reservoirs); Density Stratification and Stability. Further Reading Aeschbach-Hertig W, Kipfer R, Hofer M, Imboden DM, and Baur H (1996) Density-driven exchange between the basins of Lake Lucerne (Switzerland) traced with the 3 H-3 He method. Limnol- ogy and Oceanography 41: 707721. Fer I and Lemmin U (2002) Winter cascading of cold water in Lake Geneva. Journal of Geophysical Research 107: NO. C6, 10.1029/2001JC000828. Finger D, Schmid M, and Wuest A (2006) Effects of upstream hydropower operation on riverine particle transport and tur- bidity in downstream lakes. Water Resources Research 42: W08429, doi:10.1029/2005WR004751. Fischer HB, List EJ, Koh RCY, Imberger J, and Brooks NH (1979) Mixing in Inland and Coastal Waters. San Diego, CA: Academic Press. Hamblin PF and Carmack EC (1978) River induced currents in a fjord lake. Journal of Geophysical Research 83: 885899. Hohmann R, Kipfer R, Peeters F, Piepke G, Imboden DM, and Shimaraev MN (1997) Processes of deep water renewal in Lake Baikal. Limnology and Oceanography 42: 841855. Malm J, Mironov D, Terzhevikl A, and Jiinsson L (1994) Investiga- tion of the spring thermal regime in Lake Ladoga using field and satellite data. Limnology and Oceanography 39: 13331348. Monismith SG, Imberger J, and Morison ML (1990) Convective motions in the sidearm of a small reservoir. Limnology and Oceanography 35: 16761702. Peeters F, Finger D, Hofer M, Brennwald M, Livingstone DM, and Kipfer R (2003) Deep-water renewal in Lake Issyk-Kul driven by differential cooling. Limnology and Oceanography 48: 14191431. Weiss RF, Carmack EC, and Koropalov VM (1991) Deep-water renewal and biological production in Lake Baikal. Nature 349: 665669. Zilitinkevich SS, Kreiman KD, and Terzevik AY (1992) The thermal bar. Journal of Fluid Mechanics 236: 2742. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 1: Density-Driven Flows 255 Currents in Stratified Water Bodies 2: Internal Waves L Boegman, Queens University, Kingston, ON, Canada 2009 Elsevier Inc. All rights reserved. Introduction In the surface layer of lakes, exchange with the atmos- phere and energetic mixing from wind and convection provides oxygen and light, thus enabling growth of plankton and other aquatic life. The nutrients required to sustain surface layer ecology are primarily found in the benthos, where sediment resuspension, nutrient release from the sediments, and oxygen con- sumption occur. In the interior of lakes, seasonal strat- ification of the water column suppresses vertical mixing, effectively isolating the surface layer from the sediments. However, the stratification simulta- neously provides an ideal environment for internal waves, whose oscillatory currents energize a quasi- steady turbulent benthic boundary layer (TBBL) that drives vertical biogeochemical flux. The wave motions in lakes are initiated by the sur- face wind stress. Waves will occur on both the free surface and internal stratifying layers (e.g., the thermo- cline) and these are referred to as surface or barotropic and internal or baroclinic motions, respectively. The waves are categorized according to their length scale. Basin-scale waves have wavelengths that are of the same order as the lake diameter and are manifest as standing wave modes or seiches. Sub-basin-scale waves have wavelengths of 101000 m. These waves are progressive in nature and will break where they shoal on sloping topography at the depth of the thermocline. Characteristic Geometry and Water-Column Stratification The internal waves described in this chapter are in lakes that are not affected by the Coriolis force due to the Earths rotation: for example, small lakes in the arctic, mid-sized lake (i.e., diameter > $ 5 km) in the mid latitudes, and large lakes near the equator. These lakes have a Burger number >1. As we shall see later, the wave modes that are supported in such lakes depend upon the nature of the water column stratification. We limit the analysis to several characteristic types of stratification that are commonly observed to occur. The simplest case is that of a homogenous lake of length L and depth H, as may be typical for a shallow system or one that has recently experienced a turnover event (Figure 1(a)). During the summer months, solar heating causes a lake to become strati- fied with a layered structure consisting of an epilim- nion, metalimnion, and hypolimnion (see The Surface Mixed Layer in Lakes and Reservoirs). If the vertical density gradient is abrupt through the metalimnion, the lake may be approximated as a simple two-layer system of thickness h1 and density r1 over thickness h2 and density r2, where H h1 h2 is the total depth (Figure 1(b)). In lakes where a strong diurnal thermo- cline is present or the metalimnion is thick, the verti- cal density structure may be approximated with three contiguous fluid layers of density r1, r2, and r3 with thicknesses H h1 h2 h3 (Figure 1(c,d)). The lay- ered model for the stratification is inappropriate for shallow lakes (H< $ 15 m), where the entire water column may be composed of weakly stratified water (e.g., western Lake Erie). In these lakes a tran- sient diurnal thermocline may still occur. Shallow weakly stratified lakes are best characterized as hav- ing a continuous stratification (Figure 1(e)). Very deep lakes (with a thick laminar region between the metalimnion and TBBL) and those with a significant chemical (saline) component will also have a con- tinuous stratification beneath the metalimnion (Figure 1(f)). In general, the strength of the stratifica- tion is measured according to the Brunt-Vaisala or buoyancy frequency N g=rodr=dz p , where z is the vertical coordinate direction, g is the gravitational constant, and ro 1000 kg m3 is the characteristic water density; in the thermocline of lakes the maximum N $ 102 Hz. Surface Momentum Transfer and Wind Set-Up Wind Set-Up of the Free Surface The action of the wind across the lake surface results in frictional momentum transfer from the wind to the water (see The Surface Mixed Layer in Lakes and Reservoirs). This transfer occurs in the form of a stress (N m2 ) applied at the free surface. The stress may be parameterized as t CDraU2 10 where CD is the drag coefficient, ra 1.2 kg m3 is the air density, and U10 the wind speed measured at 10 m above the water surface. Typically CD 1.3 103 , but this value may vary by 40% depending upon the wind speed, water depth, and relative temperature 256 difference between water surface and adjacent air column. The momentum transfer associated with steady winds will push the surface water to the leeward shore, causing a displacement of the free surface due to the presence of the solid boundary (Figure 2a); for long and shallow lakes this may be as large as several meters (e.g., $2 m in Lake Erie) (see Currents in the Upper Mixed Layer and in Unstratified Water Bodies). This displacement is called wind set-up. If the wind stress is applied for sufficient time (one quarter of the fundamental seiche period as defined below), a steady-state tilt of the free surface will occur where there is a balance between the applied wind force (t surface area) and the hydrostatic pressure force due to the desire of the free surface to return to gravitational equilibrium. Balancing these forces at steady state, given the equation for the slope of the free surface @s @x u2 gH where u t=ro p is the surface wind shear velocity, sx; t is the interfacial (surface) displacement from the equilibrium position, and x is the longitudinal coordinate. The equation for the free-surface slope may be integrated to give the maximum interfacial displacement, as measured along the vertical boundary st 0; x 0; L u2 gH L 2 Wind Set-Up of the Internal Stratification In a manner analogous to the set-up at the free surface, wind induced displacements can also occur along the thermocline. Consider a simple two-layered lake. Water piled-up at the leeward shore by wind- ward drift simultaneously pushes down the thermo- cline while pushing up the free surface (Figure 2(b), Figure 3). The free surface remains nearly horizontal owing to a return flow that develops in the hypolom- nion, leading to vertical velocity shear through the metalimnion. A corresponding upwelling occurs at the windward shore (Figure 3). The steady-state slope of the free surface is given by a balance between the baroclinic gravitational pressure force from the tilted thermocline and the force due to the wind-stress acting through the epilimnion @i @x u2 g0h1 where g0 gr2 r1=r2 is the reduced gravity across the interface (thermocline) (see Currents in Stratified Water Bodies 1: Density-Driven Flows). The equation for the thermocline slope may be obtained through integration over the basin length it 0; x 0; L u2 g0h1 L 2 The effect of buoyancy can be seen by decreasing the density difference between the two layers resulting in a decrease in g0 and corresponding increase in i. r(z) r(z) r(z) r(z) r(z) r(z) H N = constant h1 h1 h3 h2 h3 h2 h1r1 r2 r1 r2 r3 r1 r2 r3 (a) (b) (c) (d) (e) (f) Depth,z N = constanth2 Figure 1 Characteristic continuous water-column stratifications as found in lakes and typical layer approximations. (a) Homogeneous water-column of constant density. (b) Two-layer approximation of the continuous stratification, where the layer separation occurs at the thermocline. (c) Three-layer approximation of the continuous stratification, where the layer separation occurs at the diurnal and seasonal thermoclines. (d) Three-layer approximation of the continuous stratification, where the layer separation occurs at the upper and lower surfaces of the metalimnion. (e) Continuous stratification throughout the water column with constant buoyancy frequency. (f) Continuous stratification where the hypolimnion is characterized by a constant buoyancy frequency. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 2: Internal Waves 257 A simple comparison s=i $ Dr=ro h1=H shows that for weakly stratified deep systems, internal dis- placements ($1100m) may be more than an order of magnitude greater than their surface counterparts ($0.011 m); for example in Lake Baikal s=i $ 0:11m=75 m $ 103 . The available potential energy (APE) embodied in the tilted interface is readily calculated for a two-layer system by integrating the interfacial displacement over the basin length APE g r2 r1 2 Z L 0 2 i x; tdx which may be integrated for the initial condition of a uniformly tilted thermocline APE 1 6 gLr2 r12 i After the thermocline tilt has reached steady state, work done by continued winds is either dissipated No flow No flow Wind (a) (b) (c) Surface seiche (V0H1) Internal seiche (V1H1) Begins Continues Maximum flow Maximum flow Wind begins Wind steady Wind stops No flow No flow No flow No flow Stops i(1) i(2) Internal seiche (V2H1) No flow No flow Wind steady Wind stops Figure 2 Movement caused by steady moderate wind stress on a hypothetical layered lake and subsequent internal seiche motion neglecting damping. (a) Horizontal mode one surface seiche in a homogeneous one-layered system, (b) horizontal mode one vertical mode on internal seiche in a two-layered system, both adapted from Mortimer CH (1952) Water movements in lakes during summer stratification: Evidence from the distribution of temperature in Windermere. Proceedings of the Royal Society of London Series B. 236: 355404 and (c) horizontal mode one vertical mode two internal seiche in a three-layered system. Arrows denote distribution and magnitude of water particle velocities. At t 0, (1/2)T1, T1, (3/2)T1, etc. the wave energy is purely in the potential form, isotherms are at their maximum tilt and there is no seiche induced flow, while at t (1/4)T1, (3/4)T1, (5/4)T1, etc. the energy is purely kinetic, giving rise to strong horizontal currents within the lake-basin and horizontal isotherms. 258 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 2: Internal Waves internally as heat or acts to mix the water column by further deepening the surface layer. Surface layer deepening has been characterized into four distinct regimes based on the strength of the stratification and winds (Figure 4 and see The Surface Mixed Layer in Lakes and Reservoirs). For strong stratification and weak winds (Regime A) the thermocline set-up is small, internal seiches persist for long times, mixing is weak and the thermocline remains sharp. If the stratification is weaker or the winds stronger (Regimes B and C), seiche amplitudes increase and become a predominant feature, shear instabilities (e.g., KelvinHelmholtz billows) form leading to entrainment of the metalimnion into the epilimnion, enhanced mixing and causing rapid damping of the internal seiches. For weak stratification and strong winds (Regime D), shear instabilities are strong; the thermocline becomes diffuse with a steep slope and rapidly deepens toward the lake bed. This creates a sharp downwind interface and a broad upwelling at the upwind shore. The upwelled fluid creates a longi- tudinal temperature gradient, which subsequently mixes the lake horizontally. The colder upwelled water is nutrient rich and as it mixes rapid fluctuations in temperature and biogeochemistry result. In deeper lakes, stratification can be strong during summer and upwelling of metalimnetic (partial upwelling) or hypolimnetic (full upwelling) water is unlikely. In these lakes upwelling is favored just after spring turn- over or prior to fall turnover when the thermal strati- fication is weak or near the surface. Wedderburn and Lake Numbers The degree of tilt of the base of the surface layer resulting from an applied wind stress may be quanti- fied using the dimensionless Wedderburn number W, which as the ratio of the wind disturbance force to the gravitational baroclinic restoring force is given by W $ g0 h2 1 Lu2 Here, g0 is evaluated across the base of the surface layer. The cases of W ) 1, W $ 1 and W ( 1 correspond to Regimes A, B/C, and D, respectively. For idealized laboratory studies and back-of-the- envelope calculations, substitution of i into the equation for W leads to a leads to two-layer form W $ h1 di where di is the steady wind induced vertical displace- ment of the seasonal/diurnal thermocline measured at the boundary. Due to the order of magnitude scaling, the factor of 2 has been dropped as is commonly found in the scientific literature. Moreover, the some- what counterintuitive nature of W ! 1 as di ! 0, leads to frequent use of the inverse form of the Wed- derburn number (W1 $ di=h1). For lakes which are not well approximated using a two-layer stratification, W has been generalized into the Lake Number, LN (see Density Stratifica- tion and Stability). This accounts for the depth Wind Negligible flow 0 2 3 4 5 6 7 m. Wind force 78 20 9 8 7.5 7.44 7.35 10 11 11.410.6 11.5 11.7 11.9 11.95 11.95 40 60 8.03 km Windermere northern basin 26 Oct. 1949. (a) (c) (b) (d) Figure 3 Schematic showing the response of a stratified lake to a surface wind stress. (ac) show the stages of development of a steady state thermocline tilt. The hypolomnion is shaded and the arrows show the relative speed and direction of the flow. (d) Isotherm distribution and temperatures in Lake Windermere, northern basin, after a steady wind for 12 h. Reprinted from Mortimer CH (1954) Models of the flow-pattern in lakes. Weather 9: 177184. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 2: Internal Waves 259 dependence of stratification and horizontal area. For a constant wind stress over a lake with an arbitrary basin shape and stratification LN St H h2 u2 A 3=2 o H hv Here Ao is the surface area of the lake and hv is the height from the lake-bed to the centre of volume of the lake. The stability of the lake St g ro Z H 0 z hvAzrzdz incorporates the variable stratification r(z) and irregu- lar bathymetric area A(z). For large Lake numbers, the stratification will be severe and dominate the forces introduced by the wind stress. The isotherms will be horizontal, with little or no seiching and associated turbulent mixing in the benthic boundary layer and interior. Changes in St with latitude and season cause LN to vary spatially and temporally around the globe. Under comparable wind conditions LN is maximal in the mid-latitudes during summer. Basin-Scale Standing Wave Motions (Seiches) Interfacial Waves in a Layered Stratification Horizontal modes When steady winds cease and the surface stress condition is relaxed, the gravitational restoring force associated with the tilted interface (water surface or thermocline) becomes unbalanced. The available potential energy embodied in the tilt is released under the action of gravity and converted to kinetic energy as the interface oscillates in the form of a sinusoidal standing waves or seiche. Antinodes are found at the basin end walls and nodal points in the basin interior (Figures 2 and 5). Seiches are com- monly called linear waves because the evolving wave-field is well described in space and time by the linear wave equation @2 @t2 c2 o @2 @x2 where (x,t) is the interfacial displacement and co the linear shallow water phase speed (speed at which the crests/troughs propagate). This equation is equally applicable to interfacial waves travelling on the free- surface or thermocline by applying the appropriate form of co gH p or co g0h1h2=H p , for the cases of surface and internal seiches, respectively. Due to the reduced effect of gravity across the thermocline rela- tive to the free surface (g0 ( g), surface waves travel at $50 times the speed of internal waves. The familiar standing wave patterns associated with seiches forms as symmetric progressive waves of equal amplitude and wavelength, but opposite sign, propa- gate from the upwelled and downwelled fluid volumes at the opposite ends of the basin (Figure 2). These waves are most commonly represented with cosine functions (Figure 5), which have central node(s) and antinodes at the basin walls. Summing cosine equa- tions for waves propagating in opposite directions, Weak stratification severe storm (a)(b)(c)(d) Regime Strong stratification weak winds Time Figure 4 Schematic showing the mixed layer deepening response of a lake to wind stress. (a) Regime A: internal waves; (b) Regime B: internal waves and slight billowing; (c) Regime C: strong billowing and partial upwelling; (d) Regime D: intense billowing and full upwelling. Adapted From Fischer HB, List EJ, Koh RCY, Imberger J, and Brooks NH (1979). Mixing in Inland and Coastal Waters. San Diego, CA: Academic Press. After Spigel RH, and Imberger J (1980) The classification of mixed layer dynamics in lakes of small to medium size. Journal of Physical Oceanography 10: 11041121. 260 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 2: Internal Waves gives the equation for the horizontal mode one (H1) standing wave pattern (Figure 5(a)) x;t a cos kx ota cos kx ot 2a cos kx cos ot The component wave amplitude a di=2 or ds=2 depending on the interface under consideration, the angular frequency o cok, where k 2p=l is the wavenumber and l the wavelength and T 2p=o the wave period. For an enclosed basin, there is one half wavelength of an H1 seiche in a lake, giving l 2L and a period of Tn 2L nco where n 1 for a H1 seiche is the number of nodal points or half wavelengths in the horizontal direction. The layer-averaged horizontal velocities associated with the H1 seiche are maximum the centre of the basin and are given by U1 g0 h2 H di L=2 t U2 g0 h1 H di L=2 t These velocities are zero at the vertical boundaries, where the motion is purely vertical (Figure 5). Similarly for the surface seiche, the mid-lake depth- averaged velocity is U g ds L=2 t The oscillatory seiche currents are low-period and quasi-steady. Observations from a variety of lakes Node Antinode Antinode Antinode Antinode NodeNode Antinode Antinode Antinode NodeNode Node AntinodeAntinode (a) (b) (c) /2 Figure 5 Schematic diagram showing the first three horizontal interfacial seiche modes: horizontal mode one (n = 1), mode two (n2), and mode three (n = 3). Arrows denote direction of water particle velocities. Solid and dashed lines denote the interfacial displacement at one-half period intervals. Upper layer velocities for the baroclinic case are not shown and can be inferred from symmetry. Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 2: Internal Waves 261 and reservoirs show the surface and internal seiche currents to have a typical range of 0.020.20 m s1 , with a maximum $0.2 m s1 during storms and to approach zero at the no-slip sediment boundary where the flow is impeded by friction (Figure 6). Higher horizontal mode seiches (n > 1) are also observed in lakes. These are described by a more general solution of the linear wave equation, where the initial condition is that of a uniformly tilted inter- face, made up of the superposition of all higher hori- zontal modes. The general solution is x; t X1 n 1 8d n2p2 cos np L x cos conp L t n 1; 3; 5; ::: n 1 for the horizontal mode-one (H1) seiche, n 2 for the horizontal mode-two (H2) seiche, n 3 for the horizontal mode-three (H3) seiche (Figure 5). An infi- nitenumber of modes are possible,each with decreasing amplitude and energy as the modal number increases. The fundamental solution is composed only of odd modes (i.e., x; t 0 when n is even) as is intuitively expected because only odd odes have a nodal point at the mid-basin location where there is zero displacement associated with an initial uniform initial tilt (Figures 2 and 3). By calculating the APE associated with each mode, it can be shown that that more than 98% of the wave energy is contained in the H1 mode, but the energy distribution between modes may be significantly affected by resonant forcing and basin shape. Examples of surface and internal seiche periods for various horizontal modes are given in Table 1. Energy will pass between potential and kinetic forms as the wave periodically oscillates with time (Figure 2). At t 0, (1/2)T1, T1, (3/2)T1, etc. the wave energy is purely in the potential form, while at t (1/4)T1, (3/4)T1, (5/4)T1, etc. the energy is purely kinetic, giving rise to horizontal currents within the lake-basin (Figure 6). For a non dissipative system, the modal energy distributions represent the sum of kinetic and potential energy and are independent of time. Dissipative processes will lead to a decrease in wave amplitude, but not period, with time (Table 1); unless there is sufficient mixing across the thermo- cline to cause a change in the stratification and hence co. For surface seiches the decay in amplitude with each successive period can range from 3% (Lake Geneva) to 32% (Lake Erie). Vertical modes When the vertical density structure may be approximated with three or more fluid layers (Figure 1c,d), in addition to vertical mode-one, hori- zontal mode-one (V1H1) seiches (Figure 2b), higher vertical mode seiches are supported; for example V2H1, etc. (Figure 2c). For a three-layer system co becomes co 1 2H g g2 4aH p where g 1 r1=r2 h1h2 1 r1=r3 h1h3 1 r2=r3 h2h3 and a h1h2h3 1 r1=r2 1 r2=r3 : 4 2 2 40 21:40 00:29 09:0003:19 Longitudinal current velocity ulong [cm/s] 5 4 3 2 1 0 Heightabovebottom[m] 23:04 01:55 04:45 05:27 06:10 07:35 Figure 6 Near-bed velocity profiles in a small lake showing the oscillatory nature and no-slip boundary associated with seiche currents. Observations are over one-half of the seiche period taken at times as indicated. The profiles are offset and are all plotted with the given velocity scale. From Lorke A, Umlauf L, Jonas T, and Wu est A (2002) Dynamics of turbulence in low-speed oscillating bottom boundary layers of stratified basins. Environmental Fluid Mechanics 2: 291313. 262 Hydrodynamics and Mixing _ Currents in Stratified Water Bodies 2: Internal Waves Substitution into the equation for the wave period Tn 2L=nco gives the period of a vertical mode-two wave, where the horizontal modal structure is defined by n. Vertical mode-two seic